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 hole into a clean, even shape if needed
Measure the opening
Cut a drywall patch to fit the opening
Install backing strips or a support piece behind the hole if the hole is larger than a small puncture
Secure the patch with drywall screws or adhesive as appropriate
Apply drywall tape over the seams
Spread joint compound over the tape and patch
Let the compound dry completely
Sand the area smooth
Apply a second coat of joint compound if needed
Sand again after drying
Prime the repaired area
Paint to match the ceiling
Reinstall any removed fixtures after the area is fully dry