First, it's far less likely than you'd think from the movies. We get giant asteroids of 10 km or so in diameter every 100 million years. Last one was 66 million years ago.
Cretaceous–Paleogene extinction event
So only one chance in a million of an event like that in any given century. And we've also found all the Near Earth Objects of diameter 10 km or larger, so that leaves just the 1% or so of asteroids that approach us from beyond Jupiter. We'd get at least a half year warning as our best asteroid detection telescopes can spot a 10 km asteroid well beyond Jupiter. And chance of an impact from them in this century perhaps 1 in 100 million.
Smaller ones are more common but are still so rare, that there are no examples in human history of anyone killed by a large meteorite.
Risk at present equal between 100 meter asteroids and the ones 1 km or larger (still yet to find 10% of the 1 km Near Earth Asteroids).
Significantly larger than 10 km, say 100 km, would be very devastating, but is so unlikely as to be impossible for all practical purposes. Not been any of those for the last three billion years as far as we can see from the cratering record on Moon, Mars, Venus (as far back as the record goes there), Mercury, and the moons of Mars.
TEN KILOMETER ASTEROID
If you wanted to survive a 10 km diameter asteroid hitting Earth - well you can look at the creatures that did survive - the mammals by going underground, birds by flying out to sea, turtles beneath the sea.
Obviously avoid the impact point, which everyone would know, go to somewhere far away, perhaps far side of the Earth.
There might be a global firestorm, so you need a fireproof shelter, and maybe a supply of oxygen just for the impact. But probably safer to go around to the other side of the Earth. Ideally to somewhere like Siberia or Antarctica with no trees to burn.
There would be an increased risk of meteorites - debris from the impact or accompanying meteorites - for the smaller ones just get underground.
Safest of all perhaps, to get into a submarine, then so long as you avoid the impact site, then not much likely to hurt you there. Tsunamis are a surface phenomenon.
Then you need food to survive the years of "nuclear winter" that follow from all the dust clouds in the atmosphere.
We'd have more than half a year to prepare, stock pile provisions etc. But much more likely to have several decades as it is unlikely an asteroid this big from beyond Jupiter would hit Earth first time we discover it, as Earth is a tiny target, more likely scenario a news report that it will hit us a couple of decades later.
It is so unlikely someone does find an asteroid this big headed our way some time this century, I think this scenario is of most interest for movie makers and science fiction authors.
ONE KILOMETER OR SMALLER
For the smaller asteroids, then evacuate the impact zone, not much more needed - the one kilometer ones have some global impacts, e.g. on weather etc, but not going to be devastating world wide.
DEFLECTING ASTEROIDS
However, given plenty of time it isn't as hard to deflect an asteroid as you'd think. Because you only need a fraction of a meter per second delta v, and over months, years, especially decades, it is easy to deflect it by more than the diameter of the Earth. And if it does flybys of Earth first, then that helps a lot as with each flyby there is a small "keyhole" of order of hundreds of meters, and if you can get it to miss that point, it will then not hit Earth the next time around.
You can also destroy asteroids, especially the smaller ones.
The priority right now though, given the limited funding for asteroid detection and deflection, is to detect them. Because the sooner we can detect them, the easier it is to deflect any that are hazardous.
And anyway, the method we need to use to deflect it would depend on the asteroid. In some cases, the easiest method would be to dust it in some white substance to make it lighter in colour - this would deflect it by a fraction of a meter per second by the Yarkovsky effect But we can't know if that's the best approach, or a kinetic impact, or "asteroid billiards" hitting one asteroid to hit another, or any of the many other ways proposed to deflect asteroids until we have an actual example asteroid we need to deflect.
The most probable news story here is not "ten kilometer asteroid due to hit Earth in six months" - that's not impossible but extremely unlikely.
A far more likely story is, say, a 50 meter diameter asteroid due to hit Earth a couple of decades from now. And if it is due to hit it in a desert or hit an ocean we might decide it is not worth the trouble of deflecting it - just make sure nobody is there at the time of impact, evacuate the impact zone.
But a 50 meter asteroid due to hit a more populated area, or a 100 meter asteroid would mean we need to deflect it, and it surely wouldn't be difficult to get the funding if predicted in plenty of time.
Both ESA and NASA have plans for a very small scale test of use of a kinetic impact to slightly change the trajectory of an asteroid, which could be scaled up if needed for an asteroid deflection scenario.
Even a ten kilometer diameter asteroid could be deflected so it avoids the Earth given enough lead time.
This is the one natural disaster we can
DETECTION DOWN TO 20 METERS DIAMETER - SAME AS RUSSIAN METEORITE
The B612 foundation has plans for a space based asteroid detection mission orbiting closer to the sun than Earth which could find the more elusive smaller asteroids quickly. It could search down to 20 meters in diameter, and would complete its first search within 6.5 years, finding most of the smaller asteroids, including ones that orbit between Earth and Sun most of the time and are harder to spot. It would cost less than half a billion dollars, which is not much, especially if it was funded internationally, and I think myself it should be a priority to fund a telescope like this, world wide. We are building many land based telescopes for astronomy that cost billions of dollars each. And frequently spend hundreds of times this much on destroyers and nuclear weapons. Can we not find the funding, somehow, for the B612 foundation space telescope? Working together, world wide? It could launch by 2018 and so find most of the smaller NEOs by the mid 2020s if the funding was available.
Since it goes down to 20 meters, the size of the Russian meteorite, we'd start to get asteroid impact predictions regularly as those smaller asteroids are so small that many burn up harmlessly in the atmosphere, sometimes not even noticed by anyone except space telescopes, especially if they hit the Earth's atmosphere far from any inhabited area. Which then could be used as tests of the methods used to predict exactly where the asteroids will impact.
SURVIVING IMPACTS BY SMALL ASTEROIDS
For those smaller asteroids the advice might well just be to stay away from windows and be wary of flying glass. Or to evacuate the impact zone if anyone is living close to the impact point. So would be easy to survive those given advance warning.
As they are also by far the most common, then if asked to guess, I'd guess that the first asteroid impact to be predicted more than a few days in advance would be a 20 meters to perhaps 50 meters diameter asteroid.
So - the sort of newspaper headlines to expect are more like:
"30 meters asteroid due to hit Earth on ..."
giving the impact point exactly - and with advice to avoid the impact zone, also probably extra flights for astronomers and other enthusiasts to go there to observe the spectacular fireball in flight from a safe distance, and locals offering accommodation for all the extra astronomy tourists, as happens with solar eclipses.
For more about this see my
Giant Asteroid Headed Your Way? - How We Can Detect And Deflect Them