Cover the edges of the drop ceiling frame with painter's tape to protect them as you work.
Stir joint compound and load it onto a 6-inch-wide putty knife.
Fill holes, cover screw holes and smooth joints in the walls with the compound. Apply it as smoothly as possibly so it is flush and even with the surface. Allow it to dry overnight.
Cover the joint seams again with joint compound and let it dry overnight. Then apply a third time. The joint compound seals the gaps between drywall sheets, making the wall surface airtight.
Sand the joint compound with medium-grit sandpaper. Wipe the sanding dust away with a tack cloth.
Paint the walls with a drywall primer using a sponge roller and cutting in the edges with a bristle paintbrush. Avoid painting the drop ceiling tiles, because you can't wash the paint off. Allow the primer to cure for at least eight hours, or according to package instructions.
Apply a water-based paint over the primer using the same methods as with the primer. Allow it to cure, then apply a second coat.
Install baseboard molding at the bottom of the walls. Measure the wall space and cut the trim to fit using a saw. Nail or glue the trim in place. Molding won't work around the top of the walls because the drop ceiling frame is visible at this point.