Remove items from the room that might block access to the high ceiling.
Cover the flooring with fabric dropcloths. Do not use plastic dropcloths, as these may hamper your ability to navigate equipment across the floor.
Access the high ceiling using a large stepladder. Cover areas of the high ceiling you want left unpainted with a low-tack professional painter's tape.
Descend the stepladder. Affix the roller frame to an extension pole. Apply a flat latex paint to the ceiling using the roller. Stand on a rolling scaffold if the extension pole is too short to reach the high ceiling.
Access the high ceiling using a large stepladder. Apply flat latex paint to areas that were inaccessible to the roller using a paintbrush manufactured for applying water-based latex paints.