Place a drop cloth under the damaged section of the ceiling. Remove any furniture from the area to give you safe access to the spot. Secure the cloths with masking tape to keep them from shifting under your ladder.
Cut out the damaged area with a utility knife until it is symmetrical. Insert the knife edge into the hole and cut in a straight line. Repeat until the section is an even square or rectangle. This cut area will need to extend to a section that includes a ceiling joist.
Measure the length and width of the hole with a tape measure. Write down the measurements.
Cut a new piece of Sheetrock with a utility knife to fit the hole. Score the back of the board with your utility knife. Snap the board over your knee to break it. Cut through the paper side with your knife.
Attach the patch piece to the ceiling joist with drywall screws. Use at least three to four screws to hold the piece in place. Drive the screw in until the head dimples the top of the Sheetrock but does not break through the paper.
Tape the edges of the patch with self-adhesive drywall tape. Press the tape firmly onto the Sheetrock.
Apply joint compound over the tape with a drywall knife. Scrape on a layer of compound that covers the tape. Smooth it out and scrape off any excess with the edge of your knife. Let this set until it is hard to the touch.
Cover the dimples with joint compound and your drywall knife. Scrape on a thin layer of compound to fill in the dimple holes from your screws. Scrape off the excess. Let this set until it is hard.
Sand the joint compound with a fine-grit sanding block. The surface should feel smooth to the touch.
Prime and paint the patched area to match the rest of the ceiling. Prime the drywall first and let this dry for four hours before applying your ceiling paint.