Remove as much of the furnishings as you can, including window coverings. Spray paint can get everywhere, so cover what you can't remove with plastic sheeting. Remove or mask off light fixtures and smoke alarms. Protect the floor with drop cloths.
Tape plastic sheeting to the walls, unless you're planning on painting them as well. Buy plastic sheeting that comes with masking tape attached so you can efficiently drape plastic from ceiling to floor.
Fill holes and cracks with spackle or paintable caulking, but don't scrape or sand it. Clean off dust and cobwebs with a broom or duster.
Spray the ceiling with at least two coats of latex paint. Wait until the paint is dry, according to label directions, in between coats. If possible, spray one coat back and forth in one direction and the next coat in the other direction.
Wait until the paint has dried for about four hours before removing the tape and plastic from the walls to ensure a clean, straight line.
Follow steps one through three from Section 1 to prepare the room and the ceiling.
Cut in with a brush around the edges of the ceiling and around light fixtures or anything else affixed to the ceiling.
Roll the ceiling. If the ceiling tiles are textured, use a 1/2-inch lambswool roller. They are expensive, but they hold more paint and get into nooks and crannies much better than synthetic rollers.
Paint at least two coats on the ceiling with the roller and brush.