Research local laws to see if you need a permit to handle asbestos-contaminated material. Wear protective clothing that you can dispose of when you are finished. It is absolutely vital to protect your entire body with bodysuit, gloves, goggles and breathing mask.
Remove all furniture from the room. Cover the walls and floors with protective plastic wrap. Turn off the power to the room where you will work to prevent possible electrical damage. Keep any air conditioning systems off to prevent spread of asbestos particles.
Spray the popcorn ceiling to make the ceiling softer to scrape. This will also make asbestos particles damp and clingy, preventing airborne matter.
Scrape off damp chunks of popcorn ceiling with a putty knife. Allow the ceiling bits to fall to the floor for later collection. If sections become difficult to remove, apply more water to soften the area.
Allow the dust to settle. Spray the plastic walls with water to get particles to stick to the plastic wrap. Spray down the plastic floor wrapping as well, and roll up the wet debris. Seal away the ceiling fragments and take all to an authorized asbestos disposal center.