As a martial artist, I'm also skeptical of the "tuck and roll" method. It seems that most times I've fallen on my bike are due to the rear wheel sliding out from under me, in which case you go down too fast and at the wrong angle to roll. If you're going over the bars it might work better.

In martial arts, the basic principles of how to fall are pretty straight forward:
Never put your hands out! As others have said, this is a good way to break your wrist.

Try to hit the ground with the maximum surface area all at once, to distribute the impact.

Tuck your head in as you hit the ground -- the force of impact will tend to whip your head toward the pavement, you want it to be moving in the other direction to
counteract that.

Oh, and stay loose.

When I've fallen on the bike I usually use something like a sideways breakfall -- the idea is to land on one side of your body, with your leg, hip, side, and arm (the side of your arm, not the hand) all hitting the ground at once to spread the impact out.

As for how to practice, I'd recommend grass or another soft surface. And it's probably best to start without the bike, just falling from a standing position. The bike has hard, pointy bits that complicate the whole process.