Place ladders or stools in the room to work from.
Use a stud finder to locate the rafters behind the popcorn ceiling. Mark the location of the rafters with a pencil; the drywall will be secured to the ceiling by fastening them to the rafters.
Measure the ceiling with a tape measure. Mark and cut drywall panels to fit, using a drywall saw or circular saw. Cut enough panels to cover the entire ceiling.
Hold the cut drywall panels up against the popcorn ceiling and fasten the panels to the rafters with drywall screws, using a screw gun.
Tape the joints where the drywall panels abut each other with drywall tape. Spread joint compound over the tape, using a wide-blade putty knife. Let the compound dry for a few hours, or as long as suggested by the putty manufacturer.
Attach medium-grit sandpaper to an orbital sander. Put on goggles and a dust mask. Sand the entire drywalled ceiling, concentrating on the joint compound to make it smooth and flush.
Apply a coat of interior primer, using a roller. Let the primer dry for two to three hours, then paint the drywall with an interior paint, using a color of your choice.