Clear the area and remove loose drywall, plaster, or debris
Cut the hole into a clean, even shape
Measure the opening
Cut a drywall patch to fit the hole
Install wood backing strips behind the opening if needed
Screw the backing strips in place
Attach the drywall patch to the backing strips
Tape the seams with drywall tape
Apply joint compound over the tape and screw holes
Let the compound dry completely
Sand the repaired area smooth
Apply a second coat of joint compound if needed
Sand again after drying
Prime the repaired area
Paint to match the wall