Lay a drop cloth on the floor to catch any debris. Scrape off the loose damaged texture from the ceiling with a putty knife. Sand the damaged area with a sanding block fitted with drywall sanding paper until it is smooth.
Fill the damaged area with drywall compound applied with a broad-blade putty knife. Smooth the repair area with the putty knife. Let the drywall compound dry completely.
Sand the repair with the sanding block fitted with drywall sandpaper until it is smooth. Brush away the dust with a soft brush. Apply a spray-on stain sealer over the repaired area. Let dry.
Apply a popcorn spray-on texture patch over the area for textures that look like popcorn or cottage cheese. Spread drywall compound onto the area and texture it with a texture brush that matches the texture of your ceiling for splotchy, swirly or other textures. Scrape off the texture with a putty knife and reapply it if necessary. Let the area dry completely.
Paint the ceiling with interior ceiling paint and a thick-mat roller to disguise the repaired area.