Wear safety glasses, dust mask, hardhat and gloves to avoid an injury and plaster dust inhalation.
Determine if lath is under the plaster. If so, drill only shallow holes or make only shallow cuts so as not to damage the lath, which are thin strips of wood used as a gripping surface for plaster.
Drill a series of holes with the largest drill bit available, spaced 1-inch apart, through the plaster, around the damaged area. Drill in straight lines to square off and frame the section. Insert a hole saw into the first hole and saw to the second and subsequent holes.
Cut through plaster using a circular saw with a masonry carbide blade. Draw straight pencil lines on the ceiling; follow the guidelines with the saw.