Always test for asbestos before attempting DIY popcorn removal. You can purchase a test kit in the hardware section of the store. If the test is positive, leave this job to the professionals.
Remove furniture from the space, or move it to the center of the space and cover with plastic sheeting. By laying down a drop cloth and plastic sheeting, you’ll protect flooring and furnishings from dust and debris and it will be easy cleanup after you're done.
Fill a spray bottle with warm water, then spray one small section (10 square feet) of ceiling at a time. Let it sit for about 20 minutes. Don’t over saturate the popcorn coating, as it could damage the underlying drywall surface.
Before touching up with drywall compound, roll up the drop cloth and plastic sheeting. Take them outside, and shake out into a garbage bin. Lay the plastic sheeting back down, or lay down drop cloths before proceeding to the next step.