To prepare the room for painting, remove furniture and other objects, including window curtains. Cover the floor with plastic sheets. Wash the ceiling with soapy water and allow it to dry. Tape the upper edges of the walls to keep paint from ending up in unintended places.
Use a 2- or 3-inch-wide paintbrush to apply white primer to the edges of the ceiling, a process called cutting in. Paint it along the edges to at least the width of the brush.
Wash and set aside the paintbrush. Dip a paint roller in the primer, wiping the excess off on the edge of the paint tray.
Begin rolling in one corner of the room. Apply the primer in a three-foot wide M shape with four strokes of the roller. Switch directions at the end of the M and make another M adjacent to the first, filling in more of the unpainted ceiling. Continue until the entire ceiling is primed.
Allow the primer to dry, which can take several hours. Wash the paint roller.
Apply white paint to the ceiling once the primer is dry, using the same techniques you used for the primer. To avoid clearly visible lines in the paint, cut in the ceiling one edge at a time if using a semi-gloss or gloss latex paint or an alkyd-based paint; don't cut in the next edge until you approach it with the roller. Continue painting until the ceiling is evenly coated.
Allow the paint to dry. Inspect the dry ceiling for paint strokes, even coloration and any sign of the previous color showing through the white paint.
Apply a second coat if necessary. Allow it to dry completely, then inspect the ceiling again. Continue adding coats until the ceiling is a smooth, uniform and clear shade of white.