What is the best method to patch a large hole (2-3 inches) in drywall?
Correct way to do it as instructed on 'Canada's worst Handyman':


cut a piece of strapping (wood) that will be a couple inches longer than the hole on each side.
put the strapping inside the hole and attach it using a couple of drywall screws so that it is across the hole. 
cut a piece of drywall that is the same size as the hole, as close as you can get
attach the patch to the strapping with a drywall screw
mud, sand, paint. 


Same process works for larger holes and also on the ceiling which can be tricky.