Put on eye protection and a dust mask to guard against particles.
Roughen a 6-inch area around the plaster ceiling damage with coarse sandpaper.
Slip one 3-inch long wood screw through the opening of one plaster washer. A plaster washer is a wide, thin disk that helps to prevent a screw from cracking plaster.
Insert the screw 1 inch from the edge of the hole or damaged area using a power drill with a Phillips head bit. Drive the screw through the plaster and into the lathe or ceiling joist until it fits snugly, but do not try to countersink the screw. Place more wood screws in plaster washers, and space those screws about 4 inches apart around the perimeter of the hole or damaged area.
Measure the width and length of the hole or damaged area. Do not try to straighten or neaten the hole by cutting or sawing off material because doing so can cause further damage.
Measure a piece of Sheetrock to match the hole’s or damaged area's dimensions, and cut it with a utility knife or a rotary tool with an all-purpose bit. If the hole has an irregular shape, place a sheet of paper against the ceiling, and press your fingers against the edges of the damage to create a rough template of it on the paper. Cut out the template with scissors, trace around it on the Sheetrock with a pencil and cut out the template's form from the Sheetrock using a utility knife.
Set the Sheetrock patch flat against the ceiling inside the hole or damaged area. Insert drywall screws, spaced 4 inches apart, through the Sheetrock and into the lathe. If the patch is small, use only two drywall screws.
Fasten a long, metal or plastic paint mixing tool to the power drill’s chuck. Push the end of the paint mixing tool into a bucket of premixed drywall joint compound, and turn on the drill to a low setting. Gradually increase the drill's speed until the joint compound is smooth.
Fill a mud pan with joint compound using a drywall seam taping knife, which resembles a masonry trowel.
Spread a thin layer of joint compound over the patched area, including the screws in the plaster, with the drywall seam taping knife. Let the material dry completely, which can take 24 hours or longer.
Measure the approximate length and width of the repaired area, including 2 inches past the screws through the plaster. Cut a piece of fine-wire-mesh screen to those dimensions with metal shears.
Spread a thin layer of joint compound over the entire repaired area. Press the fine-wire-mesh screen against the wet joint compound, and drag the edge of the drywall seam taping knife over it to smooth wrinkles. Let the repair dry overnight or until it no longer feels cold.
Apply at least one more thin coat of joint compound over the repaired area. Once it is dry, wet-sand the surface using a large, soft, grout sponge dampened with plain water. Wipe the joint compound with the sponge as if you are cleaning the ceiling until you are pleased with the texture.