Not so sure about chopping potatoes specifically, but for most vegetables, I've found there seem to be two secrets to fast chopping:
1. use a good knife, and one that is large / long enough that you can more or less leave the tip on the chopping board, and just raise the handle end, each time you chop, rather than raising the entire knife. This "rocking" motion should reduce the strain on your wrist, allow you to cut faster, and make it much less likely that the knife will slip when cutting.
2. Keep your hands out of the way! I find it best to place the palm of my left hand (I'm right handed) across the top of the blade for stability (provided you don't have a double edged blade!) and use my right hand to grip the knife handle / actually do the chopping. This way there is really no way that you can cut yourself.
As I said, this may or may not really work so well for potatoes, but it does work great for dicing onions, herbs and many other vegetables. I more or less use a variation of this technique for cutting potatoes as well, but it will probably be necessary to use your "off" hand to hold the potato steady, instead of stabilizing the blade.
Hope this makes sense!