Yes there are plans, by the Mars society. But there are many problems with their ideas.

They say it will take around 1000 years to get to the point where you can grow trees and humans can get around with oxygen breathers like aqualungs. Then another several mllennia to get to the point where you have a breathable atmosphere. Chris McKay estimated 100,000 years to a breathable atmosphere. This is all assuming mirrors in orbit to keep the planet warm along with greenhouse gas creating factories on Mars so quite high technology.

WHY TERRAFORMING MIGHT NOT BE AS EASY AS YOU THINK, OR AS IT SEEMS IN THE MARS TRILOGY

OXYGEN

First, the problem with oxygen is - that it is easy to look at the amount of oxygen that plants can produce and suppose they will create an oxygen atmosphere quickly. But plants consume as well as create oxygen in daily, yearly and lifetime cycles. And over its lifetime a plant eventually decays or is eaten and the oxygen it creates is consumed again so plants are oxygen neutral just as they are carbon neutral if their constituent carbon is returned to the atmosphere.

The most common photosynthetic reaction gives off oxygen, but also takes CO2 out of the atmosphere

BBC - GCSE Bitesize: Photosynthesis

6CO2 + 6H2O

 C6H12O6 + 6O2

So in order to build up oxygen in the atmosphere you  have to take CO2 out of it, e.g. as peat, coal, oil etc. Turns out you need to take enough CO2 out, to cover entire surface of Mars with organics to many meters depth. That's obviously going to take time.

For instance, peat accumulates at about 0.5-1 mm a year in ideal conditions, so it would take a thousand years to accumulate a meter - and that's on Earth in favourable conditions. What is peat moss?

It's also harder on Mars than on Earth because

• Light levels about half that of Earth
• Gravity about a third so  you need three times as much mass of oxygen for the same partial pressure.

So it is likely to take six times longer on Mars than it does on Earth to generate the same amount of oxygen from the same land area. And you need ideal conditions over much of the surface of Mars to accumulate all these organics.

CO2 NO GOOD AS A BUFFER GAS

Also you need a buffer gas, as high levels of CO2 are poisonous to humans, so you need to find a source for huge quantities of nitrogen before the atmosphere can be breathable. Instead of a minor constituent, the nitrogen  has to be the main constituent of the atmosphere (or some other buffer gas).

WATER

Also - it is not at all clear Mars has enough water. Yes it has water at its poles enough to cover it to a depth of at least twelve meters.

Found it! Ice on Mars

But it also has desert regions that are dry not just on the surface but for hundreds of meters down.

And the mid lattitudes are still dry for some meters below the surface, though with underlying layers of ice. There are many flow features showing that it was wet at some time in the past, but at present it is probably as dry as the Sahara (which also has water deep down).

Cydonia: Martian Mystery Region

Melt the polar ice caps and just let the water spread out and it might be like pouring water into the Sahara desert.

Yes there is water bound in the sand on Mars, as Curiosity discovered  (NASA - NASA Mars Rover Fully Analyzes First Soil Samples ), but there is water bound in the sands of the Sahara desert also, and similar amounts of water in the Sahara sands as there are on Mars. The water boiled off at 835 degrees C. Curiosity Rover Makes Big Water Discovery in Mars Dirt, a 'Wow Moment'

It's a high water content compared to the very dry moon, but not compared to Earth. And the water is bound and not available for life to use.

Even dry granite is often 3% water content r/askscience

Releasing water in the Martian ice caps for terraforming could be like pouring water into the desert sands of Sahara (here the Lybian desert) - as the equatorial regions are thought to be dry for kilometers below the surface

So, I'm skeptical that there is enough water left on Mars to terraform the planet without importing it by impacting comets etc.

Even with enough ice for twelve meters of water over entire surface of Mars, and even considering that there are also large quantities of ice buried below the surface outside of the polar regions - and that the Northern ocean bed is at a lower altitude - still is there enough to compensate for the dryness of the equatorial regions with no water for depths of hundreds of meters for most of the region?

It seems a wasteful way to use all that ice anyway if you wanted to use it to form human  habitats.

WHY SPEND MILLENNIA TERRAFORMING MARS WHEN FOR LESS COST YOU CAN CONSTRUCT A SPACE HABITAT IN DECADES?

So, personally I'm rather skeptical it is ever going to be worth doing, especially since space habitats like Stanford Torus are much easier to build and more controlled, and can be completed in a few decades, rather than in millennia.

These could be in free space, or on the Moon.

If on the Moon - then - you might need to spin the habitats for extra gravity depending on what humans need. And spinning habitats may be easier to construct in space.

Depending on what humans need for health, space habitats spinning for gravity may be easier to construct than similarly spinning habitats on a lunar or planetary surface.

WHY SPACE HABITATS WON'T BE A PLACE FOR HUMANS TO MIGRATE TO, IN NEAR FUTURE

I don't see either though as a solution to problems of finding somewhere to live on Earth - because - it is far easier to build even a Buckminster Fuller "cloud nine" city - or a sea city floating on the sea - than any kind of a space habitat. Apart from anything else, you have air to breath, and can build it or repair it without spacesuits, and can use lightweight construction, no need to hold in tens of tons per square meter of atmosphere.

Instead - I see space habitats as surely only going to arise if we have a reason to be in space. Could be tourists. Could be a retirement home. Could be space mining. Some reason why you would want to spend ten or a hundred million dollars on a home in space when you can construct the same size home or larger for perhaps a few hundred thousand dollars on the Earth.  I think we may well end up with space habitats with tens or hundreds of thousands of people eventually. But will we ever have them with millions, and billions of people?

Also you need a reason to live in space where you need to put on a spacesuit to go anywhere. I'm sure space enthusiasts will want to live in space - but - once it becomes commonplace - it will seem like living in Antarctica - the sort of thing it is cool to do for a few years but few people really want to do it full time. And even if you do have a community start up in space - the children are going to look at Earth where there is air to breath for free, and flowing streams and entire oceans of water - and everything is so much easier, and want to migrate back to Earth, I think.

AT ANY RATE TERRAFORMING MARS IS HARDER THAN YOU WOULD THINK FROM THE MARS TRILOGY

At any rate, it is far far harder to terraform Mars than you might think from the science fiction stories,  which often suggest that we could do it in a couple of centuries.

And there are many more issues involved. Here are more details:

DETAILS

First - the Earth itself took hundreds of millions of years to "terraform" -  a process we don't understand that well.

Then, after that it went into a snowball phase several times when it was almost lifeless again - and only recovered, not through action of life - but because of continental drift and volcanoes bringing CO2 to the surface.

So I think a lot of people have this naive idea - that we just need to seed Mars with life, give it a bit of encouragement, and within a few centuries, almost by itself, with a bit of guidance, it will turn into Earth, with maybe a few mirrors in space and greenhouse factories to help it along.

But even a duplicate Earth, same in all respects except without life,  probably couldn't be terraformed as easily as that. And Mars is tremendously different from Earth.

• Further from the sun - move the Earth out to Mars orbit and its oceans would freeze over turning it into "Snowball Earth"
• No magnetic field. Mars has only a few magnetic field hot spots but no protection from the solar wind.
• Lack of water - perhaps due to lack of magnetic field. Mars has lost nearly all its water.  It's believed, that it started with less water than Earth originally - but it doesn't seem to have as much water left now as it did when it had global oceans. What has happened to it remains a mystery.
  
  It does have ice at both poles, but in the equatorial regions is believed to be dry for kms below the surface as all the ice would be slowly lost by repeated sublimation towards the surface.
  
  It does have enough water, theoretically, to cover the surface to a depth of some meters - certainly enough for local flooding in high lattitudes - but if it was warmed up globally - wouldn't it all just sink into the dry equatorial regions?
  
  In any case, if we add water to it again - will lose it eventually - not known how exactly but part of the reason may be dissociation of hydrogen from H20, which then escapes to space - in upper atmosphere - because of its lack of a magnetic field to protect it.
• No continental drift - long term this returns CO2 to our atmosphere and is what got Earth out of its occasional snowball phase in the past. So if Mars turns into a snowball (which it is basically already but without the ice) - it can't get out of it again
• 40% of Earth's gravity - this means - that for the same atmospheric pressure you need nearly three times as much mass of the gas per square meter for the same partial pressure
• Orbit elongated a lot more than the Earth's
• No Moon to stabilize the axial tilt - sometimes tilts so far that it has equatorial ice sheets.

This suggests that if you did manage to terraform Mars - that it wouldn't last for long on geological timescales.

And - it's a long process also. On Earth it took millions of years.

THOUSAND YEAR LONG PROJECT

The Mars Society hope that with mega technology - giant space mirrors to reflect more light onto Mars to warm it up, and greenhouse gas factories and such like - that it could take as short a time as 1000 years - plus several more millennia to get the oxygen levels up.

But - is that what our descendants, 1000 years from now, will want us to do to Mars?

One thing that's clear - with those sorts of timescales, that we aren't doing it for ourselves.

For quite a few centuries it would be hardly changed. And all the way to the end of that 1000 years and for perhaps 100,000 years after it - you'd still need oxygen - and most of the time, need complete spacesuits to get around.

And - it's a high technology project, obviously, all the way through. So - will we maintain a high technology civilization for a thousand years to complete it? The people who want to terraform Mars often see it as a way for humanity to survive in case we lose our technology - but it's almost the opposite of that. You can't see it succeeding unless we keep a high level of technology for at least a thousand years and probably far longer than that.

UNTERRAFORMING

Then - once terraformed - it's going to gradually unterraform - the only question is how long it takes - at least - unless you keep supplying comets to replenish the atmosphere - if so - sustained long term megatechnology.

What seems pretty clear is - that nature won't just keep it terraformed for us automatically. What we see on Mars is the end result of Mars which might well have had life in the past.

And Earth's biological cycles, which keep Earth terraformed, won't work on Mars because of the cold, lower gravity, and long term - lack of magnetic field and continental drift.

I don't think that necessarily means it is impossible. But means that any solution to terraform Mars would need to take account of all these differences - and also need to look into the future - and decide - are we doing this for our descendants 30 generations from now? Or perhaps 30,000 generations from now if you allow an extra 100,000 years to build up an oxygen atmosphere on Mars?

If so - why? And will it matter for them that Mars would unterraform? What would the implications be for our descendants even further into the future, say a few 100,000 generations from now, as Mars loses it's atmosphere again and its water and returns to its current lifeless state, or some other state?

RESPONSIBILITY TO OUR DESCENDANTS

With the Mars society plan, we are doing this to help our descendants perhaps 30,000 generations from now (100,000 years). If doing it that way, then we probably should also think about our descendants 300,000 generations from now (a million years or so)

I think we have a responsibility to those far distant people - who - well won't be exactly people as in that they will have evolved to new species long before then - but whatever or whoever they are - are stuck on a planet that we attempted to terraform which is gradually unterraforming around them - and may well have lost their technology by then.

It's an awesome thing to change the entire future of a whole planet - even if it does work. Especially also since - maybe if you set about things in a different way, using knowledge we don't have yet, but might have, say a century from now, maybe the whole process could be made far easier and take a shorter time to a better end result.

There is no hurry to get started on a 1000 year project, not if it is not yet totally clear that it's the best thing for us to do.

That needs to be thought through first!

And - lots of things to go wrong.

See my Trouble With Terraforming Mars
And
Imagined Colours Of Future Mars - What Happens If We Treat A Planet As A Giant Petri Dish?

But who knows - in the future maybe we might do projects like this. Not impossible, in a long stable civilization - and maybe with lifetimes extended, people living for tens of thousands of years etc etc, then you might get the understanding and knowledge needed to do stuff like this - and also to understand its consequences.

I think is great to think over ideas -but to actually attempt it now - especially - in some simple minded way just throwing microbes onto Mars and hoping they turn it into a copy of Earth - that's not going to work. And adding mirrors and greenhouse gases - again - just too crude, when we don't even understand how Earth works too well, and Mars is so different - and so much to go wrong.

PARATERRAFORMING MARS

We could paraterraform Mars - cover it with greenhouses. It's another future possibility which may seem less controversial. You have humans living there right away (assuming we can stand the low gravity that is) - and eventually they spread out over the surface of Mars. In effect this is what SpaceX and Mars One intend to do, a tiny start on paraterraforming Mars - putting habitats on the planets for humans to live in.

But I think we should think long and hard before deciding to do that also - because it also is irreversible.

The thing is, as soon as you introduce life to Mars - you start to transform the planet, and at our present level of knowledge of both Mars and life - results would be unpredictable. Even if you only intend to live in greenhouses, still life would escape your habitats and there seems at leaste a reasonable chance of various potential habitats for life on the surface of Mars. If they exist, eventually life would find them.

And we don't know enough to predict what would happen, how life would transform Mars - not at all clear that it would transform it in a way that humans would like.

And we only have the one Mars in our solar system. Once we have done something irreversible to it -we can't roll back and start again.

There may well be other Mars like planets in our galaxy - but they are many light years away if they exist, and we can't hope to get to them in the near future. So we can't "replace Mars" with a new planet, if we experiment with it and our experiment is a failure.

WHAT WE CAN DO INSTEAD

I think that it is far too soon to think about migrating away from Earth, if we ever do that. Instead focus on exploration and discovery. And go to space when there is a reason to be there.

In particular, the Moon is close to Earth, far easier to recover from disasters, accessible to tourists, has more resources than we thought before.

As well as that the Near Earth Orbits are numerous with many resources that could be used to construct space habitats, and of far more interest than we thought it was.

And we can build spaceships to travel to the other planets and Antarctica type settlements to study them from orbit - once we have the capability to do this. I think that is still several decades away myself - SpaceX may be able to handle the engineering to get mass of humans to other planets - but reliable closed system habitats for humans to live in for years on end may be another matter.

However, I see n problem with it in principle - so long as it is done with care not to contaminate them with Earth life.

The Moon is the obvious starting point though. And is far more interesting than you might think. If you find the Moon boring, chances are that you'd find Mars just a boring once the novelty wore off.

Things we can do on the Moon:

• Construct radio telescopes on far side in radio quiet zone to observe universe in the many radio frequencies that are not available on Earth because of noise from human communications, mobile phones, microwave ovens, tv and radar etc.
• Search for meteorites from early Earth - the giant meteorites that hit early Earth must have left remnants on the Moon. These surely also include remains of early life when it was just starting to evolve. Later rocks will have ammonites, trilobites etc in fragments. They are probably going to be hard to find, many of them buried deep. But what a huge amount we could learn from them? Meteorites that hit the polar ice regions might still have intact organics, if buried deep enough.
• Examine the ice at the poles of the Moon - this may preserve a record of the entire solar system history much as the Antarctic ice preserves climate history.
• Mining the ice and He3 - but with care. There is enough ice there - perhaps - so that we could supply all the water we need for decades and not make a noticeable difference to the amounts. But would the mining operations themselves have adverse effects on the Moon. As for the He3, it's for a future technology not yet developed - and strip mining surface of the Moon may well be too invasive to consider, especially if we can use solar energe instead
• Solar energy - are ideas to construct solar panels around the equatorial region of the Moon, continuous strip so you supply energy 24/7 to the Moon and also beam it back to Earth.

As for Mars, it is of great interest I think, but not as a place to terraform or colonize, at least not right now. It is just not that good for humans.

But - I think it is a fascinating place to explore and may contain many answers to puzzles about the origins of life. I think it needs to be explored like the Antarctic lakes below the ice surface - with great care not to contaminate it with Earth life. That suggests continuing to explore it by missions from the Earth - or else by telepresence from orbit around Mars. At least until we know more about what is there and what effect Earth life would have on the planet.

And the best people to explore Mars long term right now I think are exobiologists. That is if there is life there. With support staff of course. But they will be the ones motivated enough and interested enough. Geologists also. They will find it endlessly fascinating while the rest of us, after novelty wears off, would just see lots of grayish reddish rocks that each look much like the other to untrained eyes.

Take the photos of Mars and imagine that someone told you this is somewhere on the Earth not on Mars. I.e. take away the novelty aspect of "this is Mars" from the scene. Then add, that this place is so heavily polluted (say) that it is impossible to go out of doors without a spacesuit. And that you have to build your buildings with few windows and heavily constructed as the place has lost most of its atmosphere.

Would you want to live there? Surely not. Though you might want to visit it for a while.

This question has been asked several times in different ways so editing my answer from those to create this one:

What is the most cost effective way for us to terraform Mars?

Robert Walker's answer to Can any of the planets of the solar system be terraformed for human habitation?