Cover any furniture in the immediate area near the peeling ceiling with plastic sheets. Remove any curtains or drapes, along with any wall artwork, near the peeling ceiling area. Tape plastic sheets along the edge where the ceiling meets the wall, with the sheets hanging down to the floor. Be sure the plastic covers any nearby windows.
Place drop cloths on the floor underneath the peeling area, and place a step ladder underneath the peeling spot.
Put on goggles and a dust mask as face protection. Climb the ladder, and wipe the peeling area with a wet sponge, to soften the texture.
Scrape away the peeling ceiling texture down to the smooth drywall surface underneath it, using a ceiling texture scraper. Scrape the texture from ceiling corners with a small putty knife. Scrape an area about 3 inches around the perimeter of the peeling spot.
Wipe away any remaining debris from the ceiling, using a rag. Examine the ceiling for any signs of water damage or water stains. Make any repairs, as necessary.
Coat the ceiling area where you removed the texture with primer, using a paint brush or roller to apply the primer. Allow the primer time to dry, according to the manufacturer's instructions.
Put on rubber or latex gloves. Spray an aerosol-spray texture onto the scraped ceiling spot, overlapping the outside perimeter just a little. Avoid spraying too much texture in one spot.
Glide a drywall taping knife along the sprayed area to scrape away any over-spray, so that it matches the rest of the ceiling texture.