How do you keep eye glasses from falling on a 4 year old?

Proper fit and strap. The two most proven ways are #1: make sure the frame properly fits his/her face. If the frame is contorted, it needs to be adjusted and if it is not a proper fit for the child's face, it will never stay on the face. #2: a strap can be placed on the temple pieces to go around the back of the head to keep them in place.
It can be tricky. The most common cause for eyeglasses to fall off a young child is the child's refusal to keep them on. Aside from a comfortable fit, proper prescription, a sports-type strat, and light frame and lenses, constant encouragement and keeping your child's mind off the glasses are the most important methods to allow successful glasses wear.