When you watch professional chefs chop, their hands do a lovely dance that is not that different from tango. The knife hand is the one that gets all the attention. I bet that's what you are looking at when you watch food TV. That's Ginger. It's showy and flashy, but that's not where the speed and accuracy comes from. It comes from the guiding hand. It seems like it just sits there on the vegetable doing nothing. But look closer and you'll see how complex its job is. It holds the vegetable in place and leans against the knife blade telling it where to land. All the knife hand has to do is go up and down in a rhythmic pattern and somehow the slices come out all even.
How does the guiding hand manage to produce slices that can be as thin as paper? Just like Fred did -- full body contact. If you are thinking that it's easier to be pressed against another warm body than a sharp knife, think again. Both are hard. In one case, you feel like you are going to trip each other and fall; in another, like you'll chop your fingers off. Neither usually happens, and if you conquer your fear, you'll be amazed how much your dancing or chopping will improve.
Here is a video I just made of how to use the claw grip correctly. It will help you with slicing and dicing absolutely everything -- from an onion to bok choi.
Sept 6, 2011 update: I have recently made a new and improved claw grip video, which I put into this post instead of the original video.
p.s. by the way, I don't think I ever went through as many band aids whiles learning to chop as while learning to dance. No, it wasn't from my partner stepping on me. It was from excruciatingly painful high heels.