The biggest thing to remember is to keep your arm relaxed. If it tenses up, you'll lose control.

Personally, I anchor my hand on the bridge, the pick lightly grazes the strings, I use a Fender heavy pick and hold it with thumb & 1st finger.

I've heard Kirk Hammett say only your wrist should move, but when I play really fast, my whole forearm locks at the wrist and moves at the elbow, which isn't terribly good, but I can't help it.