Turn off power to any ceiling fixtures near the hole
Cover the floor and furniture with a drop cloth
Remove loose drywall, plaster, or debris around the hole
Cut the damaged area into a neat square or rectangle if needed
Measure the opening
Cut a drywall patch to fit the opening
Install backing strips behind the hole if the patch needs support
Screw the patch into the backing strips or ceiling joists
Tape the seams with drywall tape
Apply joint compound over the seams
Feather the compound outward with a wide putty knife
Let the compound dry completely
Sand the patched area smooth
Apply a second coat of joint compound if needed
Sand again after drying
Prime the patched area
Paint to match the ceiling
Clean up dust and remove coverings