Move items away from the walls. Protect all your furniture and floors with dropcloths.
Cut in at the ceiling first, painting with a brush the corner joints at the ceiling-wall juncture. Use flat paint. Paint both the wall and ceiling side of each joint to save time.
Roll the ceiling. It's important to work from high to low points in the room.
Cut in the joints where walls meet. Cut in around windows. Cut in other trim areas, such as baseboards and around doors.
Roll the walls. Start high on the walls, painting a few square feet per roller load.
Paint trim with a brush and semigloss paint. A paintbrush with an angled edge helps with corners. If you get a bit of semigloss on flat paint of the same color, rub the wet paint off with a rag. Your small mistakes won't be visible in the finish.