When decorating a room, painting the ceiling should ideally be the first job you do, so the paint does not drip onto other surfaces. If you only want to paint the ceiling though, this video will explain how to.
To get started you should paint the ceiling first to avoid getting paint on the walls or woodwork. To get started, cover the floor with a dustsheet and remove all furniture or place it in the middle of the room.
Cut in at the edges using a 2 inch brush. Use the brush on its edge and work in long sweeping movements.
After you have cut in, finish the job with a roller attached to an extension pole, dampen the roller first to help it pick up the paint. Start in one corner, applying with a W motion. Work in square sections across the ceiling, overlapping each one by a third.