Smart shaving just the "easy" portions of your face to start. If your hands seem to be getting in the way try using both hands. Right hand for right side and left hand for left side. Take your time, go slow, and I think you'll find switching hands is a big help, and I'm not ambidextrous by any means.

Oh, yeah. A lot of cuts come from "resting" the blade on your face. If the blade stops all it takes is a very small movement to the side to cut yourself. Keep the blade moving and lift it off your face at the end of the stroke.