Well depends on whether you are Hindu or Buddhist I think (or indeed Jain or any other religion that has this idea). I can only answer from the Buddhist perspective.

According to Buddhist teaching, you can't really, as we have countless past good and bad karma. We can add to both. The bad karma can only be got rid of by exhausting it, experiencing the harmful effects. Which is a process that can never end as there are vast amounts of both bad and good karma from the past.

Except perhaps in some tantric traditions in Tibetan Buddhism where they claim to be able to purify your past karma. But I don't understand the details of that. So won't talk about that.

As ordinarily understood, e.g. in Therevadhan traditions and most Mahayana traditions, then Buddhists don't aim to get rid of all their past negative karma, or to balance it with good karma. I think that's more a Hindu idea.

The good karma is useful though because it helps you to a more stable situation. It can also lead to some temporary pleasure in Samsara and there is nothing wrong with that either. The lowest aim you can have in the Buddhist teaching is to aim to have a more fortunate life in the future, and more stability and happiness in this present life. Although considered "lower" it is still more than most do, and it is considered a worthwhile thing to do.

After all if you have compassion and loving kindness, you aim to help others to find a way out of suffering and to find happiness, so you'll rejoice if they find some fortunate state in Samsara even if this is just temporary relief for them.

But even good karma in this sense still binds you to Samsara, to the cycle of repeated birth, old age, sickness and death and all the other forms of unsatisfactoriness, that our "happy ever after" somehow never quite lasts for ever.

Then also if you can find some stability, then there's a chance of connecting to teachings, either by teachers, or indeed you can also get teachings from the natural world, and also in ways that are hard to explain, for instance from contemplating a Zen koan, or from the experience of the pure nature of compassion or wisdom and other good qualities (rather like the experiences in various mystic traditions in different religions).

The four noble truths are about a path to cessation of suffering and unsatisfactoriness.

The third truth is the path to cessation which is presented as the noble eightfold path. That's mainly to do with creating some stability so that you can then have a chance to see the truth for yourself, directly. In the mahayana traditions they may focus instead on cultivating the paramitas or boundless qualities such as loving kindness, compassion, etc.

Once you have stability, then the path is gradually dawning understanding and awareness. To do with continually relating to the truth of whatever situation you are in, not blinkering yourself with illusions. And then finally you see all the way through the deepest illusion and confusion. Which according to Buddha's teaching is something to do with attachment to views of a self that are not in accord with the reality of what we are and how we are.

And though hard to spot, according to these teachings, it's also in some ways the most obvious thing there is, It is hard to spot because it is so obvious and familiar that we no longer notice it.

When you see the truth of your situation, then he taught, you then reach cessation of suffering. Right away.

What that means is hard to understand intellectually. After all he still got old, and experienced sickness, and eventually died. In what sense had he realized cessation of suffering and unsatisfactoriness as a young man?

Anyway he said you need to see this truth for yourself. So that's the path. And realization of cessation can happen in this very life, and is not a heaven state that you enter when you die. There is no idea of heaven in Buddhism - there are ideas of more fortunate rebirths, which may be in states where you are blissfully happy for trillions of years, but if such rebirths exist, they are still just part of samsara, temporary states, which you eventually fall back out of. So even they are not a "happy ever after".

That is why just accumulating positive karma does not free you from samsara in Buddhist teaching. It's worth doing, and you will do it anyway as you develop clearer understanding of your situation. Being more open, compassionate, showing loving kindness etc all tempered with wisdom in the Mahayana traditions, or being less focused on yourself, and open to every situation you meet in the Therevadhan approach - all that will accumulate good karma, and help others also to accumulate good karma. But that's considered a lesser aim in the Buddhist path because of this idea that there is no "happy ever after" that truly lasts for ever in samsara and that accumulating positive karma is not a permanent solution, and indeed, is yet another thing to bind you to samsara even though binding you to happy future states.

MINIMAL EXPERIENCE OF PAST KARMA

Also just to add, though as normally understood (I don't know about the esoteric tantric traditions), you can't purify past karma without experiencing it, you can often experience it in a minimal way. And you can also stop minor effects of past bad karma from blowing up into a major thing.

For instance if I get hurt by something, say stung in your leg and the sting goes septic - that's a result of past karma that I'm born in a body that is vulnerable to harm like this. (In Buddhist teaching then it's not "tit for tat" where e.g. a mosquito bites you on the nose, that means that you bit it on its nose in the past. It's much more intricate than that and also depends on present day decisions by yourself and others too).

But you can go to a doctor and get that damage to your leg healed. Maybe he or she will prescribe a course of antibiotics, for instance. Or whatever it is they do in that situation. Or you can just not tell anyone and it gets worse and worse, maybe when you finally go to a doctor, your leg needs to be amputated.

Similarly if you get irritated by something (again something that results from past karma, that you find it irritating), you can either let yourself get more and more angry until you are in a full rage about it, or you can just let it pass, related to it as best you can, and it may come to nothing much.

If you go into the details here it is very intricate and complex however. It's said to be far harder to understand the interdependence of beings and conditions than it is to begin to see through the attachments you make to false ideas of a self.

IMPOSSIBLE TO ELIMINATE PAST KARMA IN THIS LIFE

I think it’s reasonably obvious that you can’t eliminate all effects of past karma in this lifetime. Amongst those effects are this body itself. It’s vulnerable to harm from trauma, from heat or cold, lack of oxygen, chemicals, many other hazards. It’s also subject to sickness, old age and death.

If you could remove all the effects of past karma in this lifetime, your body would have to be invulnerable to any harm whatsoever.

Even Buddha got old, experienced sickness and death after his enlightenment.

So becoming enlightened doesn’t mean you eliminate all effects of past karma.

But you do transform them. After he was enlightened, then his past interactions with other beings became the thing that made it possible for Buddha to interact with others and teach them for another 45 years. It is what made it possible for him to continue to have a human body after enlightenment.

In the traditions like Tibetan Buddhism that talk about emanation bodies and Buddhas able to reincarnate multiple times after enlightenment, even many times at once, again those physical, human, emanation bodies are due to past interactions they had with other humans before they became enlightened.

What you actually call it after enlightenment I’m not sure, again maybe someone here can elaborate, but it’s the enlightened version of karma. Basically, interdependence.

So, I think that’s true even in the esoteric teachings in Tibetan Buddhism. They do talk about purifying past karma. But I think it may be more like a transformation than actually removing it. But don’t want to say more about that, maybe others who know more about that can elaborate.