Lama Ole’s answer:
You outsmart the thing by its own means. Buddhism is a method of constantly outsmarting the ego. You have to use the energy of the ego—the illusory, non-existent ego—in order to get to where it is no longer there. So you use this idea of a self to purify the veils until there is no more ego illusion.
The ego is very strong, but it is also stupid. There are some great teachers in the history of the Karma Kagyu lineage who worked directly against the ego. The story of Milarepa and his teacher Marpa is particularly well known—that was still a really tough school. But most of the time, one has to give people something sweet at first. The ego then thinks, “Ah, not only am I a good guy, but now I’m also getting spiritual.” One then keeps this good feeling as long as possible.
Later, the ego slowly discovers that it gets a lot of bread and potatoes but little meat and vegetables. One now belongs to a noble family. Especially with me as a teacher, it is clear that I like a “stiff upper lip” and good style, and that I don’t like to see drama and weakness. Suddenly, the ego can’t play all the games it used to. It can’t build itself up anymore through powerful feelings like, “I hate him,” “I am the best,” “I am the worst,” and so on.
Seeing that it’s not doing so well, the ego then tries to protect itself by all means. For example, it projects feelings, or a sore back, or thoughts like, “I am constantly getting worse!”—which is not true at all. It’s just that one can suddenly see how one has always been. In this difficult situation, we throw another piece of meat to the ego—for example, the bodhisattva attitude. We tell it, “You are here to help all beings.” At first, the ego thinks we’ve noticed how good it is and all the things it can do, but actually the bodhisattva attitude is complete poison for it. First, we have to think of others all the time and therefore have no more time to think of ourselves; and second, we always get those teachings on emptiness, which say that we don’t exist at all.
This is really fatal for the ego. Now it has already become so weak that it has only one place left to entrench itself. That’s when it starts to see what others are doing wrong. It has already given up trying to protect itself, since it knows that everything is actually an illusion. Now instead it tries to find faults in others—“He does this and she says that,” and so on. How do we conquer this final bastion? How do we make the ego smolder and finally snuff it out completely? Through the pure view! We think, “Even my doubt is my buddha nature. Even my most evil thoughts are spontaneous wisdom. My biggest problem is my best way out.” Then we’ve made it.