Cut the damaged area into a clean square or rectangle
Remove loose drywall and debris
Measure the opening
Cut a drywall patch to fit the hole
Install wood backing strips behind the opening if needed
Screw the backing strips into place
Attach the drywall patch to the backing strips
Apply drywall tape over the seams
Cover the seams with joint compound
Let the compound dry completely
Sand the area smooth
Apply a second coat of joint compound if needed
Sand again after drying
Apply a third thin coat if needed
Sand the final coat smooth
Prime the repaired area
Paint to match the wall