Understanding "no self" does not come from destroying something we call "self" or "ego". The great awakening or discourse of the Buddha revealed that there was no self, no permanent I, to begin with. So if there is nothing we have to get rid of, then understanding selflessness very simply comes from careful awareness of what actually is happening moment to moment.
It does not take too long to get a beginning sense that appearances arising in consciousness are not self, because we see how they just keep coming and going. A subtle identification can still take place, however, with the knowing faculty itself: "I'm the one who's knowing all these changing objects." We might believe the knowing I, is self. Because knowing, or consciousness, is much more subtle than other arising objects, you might find it difficult, at first, to be mindful of it. But as the mind's power of steadiness, stillness and clarity grows stronger, we can actually become aware of awareness.
At certain stages of meditation practice, it becomes clear that consciousness itself is a changing process. This discovery can be unsettling, because for so long we have identified with the faculty of knowing as being most essentially who we are, taking it to be our soul, our self, our center. And now we see that it, too, just like all other phenomena, continuously appears and passes away.
Imagine yourself dropping out of an airplane and free falling for the first few minutes. Imagine the sense of exhilaration. But then you realize that you do not have a parachute, so you panic as you fall through space. Falling, falling, falling, filled with terror that you do not have a parachute . . . until a certain moment arrives when you realize that there is no ground! At that point of understanding, you just enjoy the ride.
We often go through a similar emotional sequence in meditation practice. As our identification with things loosens up a little, and we see the rapidity of change, at first there can be real exhilaration, a greater sense of spaciousness. But feelings of panic can come when we realize that there is nothing at all to hold on to. Both the objects of awareness and the faculty of knowing are continuously falling away, like a river over a waterfall. We understand now, on a deeper level, that nothing we grasp at for security actually provides it. But as we continue with the practice, enlightenment dawns; there is no ground to hit and no one to hit it - just empty phenomena rolling on. Then we feel the great relief of letting go, the deep feeling of equanimity, and the joy of ease.