Check the ceiling for asbestos before you attempt to work on it. It's best to have it tested by a certified contractor who deals with this type of problem. If your ceiling has asbestos, it's best to have it taken care of by a professional. If the ceiling is asbestos-free, you can continue to work.
Mix a solution of one part white vinegar to three parts water in a spray bottle. Put the cap on the bottle and shake it to mix the ingredients together.
Set up a ladder in one corner of the room. Spray a 4-foot square area of the ceiling with the vinegar solution. The ceiling should be thoroughly moist. If you're lucky, the popcorn finish will begin to fall on its own within a minute, but this isn't likely on any ceiling that has been painted over.
Scrape the popcorn finish off the ceiling with a putty knife.
Move the ladder over to a new position and repeat the process. Continue this until the entire ceiling is finished.