Remove all the furniture from the room or area of the room where the ceiling is being repaired. Cover the floor and any remaining furniture with plastic sheeting.
Cut out the affected area of the ceiling using a utility knife or punch saw. If the entire ceiling is not being replaced, cut out the moldy section as square as you can and expose a ceiling joist on both sides. Ensure that you remove all moldy and damp ceiling material. Place ceiling debris in a large garbage can lined with contractor garbage bags. Tie and remove the bags as they are filled.
Clean off screws or nails from the ceiling joists using an electric drill with a driver bit installed or a claw hammer. Ensure that the surface of the joists are free of any of the old ceiling material.
Measure the area being repaired if it is not the entire ceiling. Cut a piece of drywall to fit in the section of ceiling being replaced, using a utility knife. Cut the drywall on the paper side and use a straightedge to achieve an even cut.
Install the drywall onto the ceiling using 2-inch drywall screws and an electric drill with a driver bit installed. Insert the screws with the drill through the drywall and into the ceiling joists every 12 to 16 inches. Drive the screws until the heads are flush with the surface of the ceiling.
Lay self-adhesive drywall tape evenly over all the seams.
Spread joint compound on the seams using a 6-inch drywall knife. Use the knife at a low angle to the ceiling to spread the joint compound and at more of an angle to remove the excess joint compound. Cover the entire seam but make the joint compound as smooth as possible. Let the compound dry for 24 hours.
Sand the joint compound using a drywall sanding screen installed on a pole sander. Lightly remove ridges, bumps and high areas of dried joint compound. Repeat the joint compound application with a 10-inch drywall knife and sand again after the second coat dries. Paint or texture the ceiling according to your preference.