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 opening
Install wood backing strips behind the hole if needed
Screw the backing strips to the existing drywall
Place the patch into the opening
Screw the patch to the backing strips
Apply drywall tape over all seams
Spread joint compound over the tape and screw heads
Let the compound dry completely
Sand the dried compound smooth
Apply a second coat of joint compound
Let it dry completely
Sand again until smooth
Apply a third thin coat if needed
Sand the final coat smooth
Wipe away dust
Prime the repaired area
Paint to match the wall