Place a drop cloth on the floor. Set up a sturdy ladder.
Scrape away any loose paint and plaster on the coved ceiling with a putty knife.
Sand the ceiling, using a flexible sander in the curved area of the ceiling.
Wipe the ceiling with a damp microfiber cloth to remove all of the dust left behind from sanding.
Prepare the joint compound as directed. Use a putty knife to fill the cracks and holes with the compound. If the damage is deep, you will need to apply two to three layers of compound to build it up; allow each layer to dry for at least 30 minutes.
Sand the dry joint compound with a flexible sander. Step down from the ladder every couple of minutes as you sand to visually check your work. Wipe away the dust with a microfiber cloth when you're finished.
Prep the walls for painting. Apply a coat of primer, using a long-handled paint roller on both the walls and the ceiling. Make long, continuous strokes from the wall to the ceiling. Allow the primer to dry overnight, or as directed by the manufacturer.
Apply two coats of paint to the walls and ceiling.