Depends how big the hole is. If it's a small hole
1" or less you should be able to patch it up with some drywall mud. If it's bigger that that your best bet is to cut out a square or rectangle(witchever is more applicable) and get a new peice of drywall and and cut it to the same size as the cut out. You will have to attach a peice of wood to the edges of the cut-out for achoring of the new peice. Just run some drywall scres into the wood from both the old wall board and new.
Good luck