Tape down dropcloths over the flooring in the room. Any furniture in the room should be removed.
Find the ceiling joists with a stud finder by moving the stud finder back and forth across the surface of the ceiling. It will indicate either with a laser or on the screen where the studs are located. Mark their location with a pencil.
Cut through the bad drywall on the ceiling with a utility knife. Try to keep your cuts straight to make the patching process easier. Remove all of the bad drywall. You may find bits and pieces of drywall attached to old nails on the joists. Brush this off and remove the nails with the back of your hammer.
Hang new drywall panels up with a cordless screwdriver and drywall screws. You will need someone to help you hold the panels up while you attach them. Use 2-inch drywall screws and screw them in through the panel until the head of the screw dimples the surface of the drywall.
Tape your seams with self-adhesive drywall tape. Apply the tape and press it firmly between the panels.
Mud over the tape with joint compound and a drywall knife. Scrape off the excess compound as you work. You only need a thin coat.
Sand the compound smooth with a hand block sander in a fine grit. The surface of the drywall should be smooth to the touch. The compound should be flush with the rest of the panel. Let the compound set according to manufacturer instructions.
Prime the patched spots on the ceiling with a latex primer. Roll the primer on to get an even coating. Let this dry for four hours.
Paint over the primer with a textured roller and/or textured paint. Roll on the texture. Feather your edges with the rest of the ceiling to blend in the patch.
Spray on a texture. Alternatively, you can use a textured spray paint to match the texturing on the rest of the ceiling. Feather your edges to blend the patch.