Protect the floor with a drop cloth--popcorn texture can get messy. Move furniture away from the damaged area, or cover it with a drop cloth. Wear safety glasses and a dust mask.
Use a putty knife to scrape away all of the damaged or flaking texture. Use your other hand to hold a square of cardboard underneath the area that you are working on to catch the debris. Scape away the texture a few inches outside of the damaged area as well.
Secure a plastic tarp around the damaged area with pushpins. The tarp should be about a foot away from the damaged area and should hang down 4 feet. Spraying the popcorn texture is a messy task and will get on anything that isn't protected by the tarp.
Use a spray-on primer that blocks stains on the damaged area. Allow the area to dry.
Shake the can of acoustic texture for a few minutes. Hold the spray can straight up about 10 to 15 inches from the damaged area. Cans of spray-on acoustic texture are available at your local hardware store.
Apply the texture in short, thin bursts using a sweeping motion. Allow it to dry. If necessary, apply a second or third coat until the area matches the existing ceiling. Allow the repaired area to dry for at least 24 hours.
Paint the area to match the rest of the ceiling. In some cases, it may be necessary to paint the whole ceiling to fully conceal the repaired area.