Two types of plasterboard repairs may be needed. If it's a small area, a bit of joint compound or spackle can fix it. But if the area is larger, a piece of plasterboard will have to be replaced. Ceiling plasterboard is 1.5 cm (5/8 inch) thick and a large area can be quite heavy -- a 1.2 by 2.4 m (4 by 8 foot) sheet weighs 34 kg (75 lb). Consider the size and whether you are physically comfortable with taking down one piece and putting up a new one.
For a small repair, scrape around the damaged area with a tradesman's knife to remove loose material. Apply mesh tape (it is sticky on one side). Spread a small amount of joint compound over the tape with a 15 cm (6 inch) plasterboard knife. Wait for it to dry and sand. If a second layer is required, apply it, wait for it to dry and sand before priming and painting. Larger damaged areas need to be cut out and replaced.
For a larger repair, use a stud finder to locate the ceiling joists on each side of the damaged area. Mark along the joist centres with a long pencil line (two pencil lines will be parallel). At 15 cm (6 inches) each side of the damaged area, mark pencil lines across to create a square (or oblong) outline.
Run a tradesman's knife a number of times along the outline until it contacts the two joists and cuts through the plasterboard on the other two sides. Remove the section (some screws in the joists may have to be taken out). Cut a new piece of plasterboard the same size. Insert the new plasterboard into the hole, screwing it into ceiling joists with 4 cm (1 5/8 inch) plasterboard screws every 20 cm (8 inches).
Cover all joints with mesh tape. Apply joint compound with a second layer if required. When you are happy with the smoothness/finish, prime and paint to match the surrounding area.
Make sure your ladder is placed firmly on the ground before use. You may want to stretch both back and arm muscles before installing the new plasterboard.