Set up for the repair job. Remove all furniture from the room and lay down plastic drop cloths. Put your protective gear on and set up the scaffolding underneath the area that needs to be repaired. While you can use a ladder, a scaffold gives you a more secure surface and makes it easier to get the job done.
Cut or chip away the area around the damage. You will need a relatively straight area to patch the ceiling. Cut away any jagged drywall around the damaged area, or knock down the plaster or tiles until you have a relatively square hole to patch.
Cut a panel to fit the patch area if you are replacing drywall or plaster. Screw it into the ceiling joists with drywall screws and a drill. Put a screw along the joist every 12 inches. Screw it in enough to dimple the drywall. Tape and mud around the edges and in the dimples. If you are plastering, apply a skim coat of plaster over the drywall. If you are repairing ceiling tiles, insert new tiles into the grid.
Let the drywall mud or plaster set. Plaster sets up in less than 30 minutes, but drywall mud will need a few hours to dry. Once the medium is set, sand it smooth with a fine grain of sandpaper.
Paint the patched area in the same color as the rest of your ceiling. The repair should look seamless.