Remove all the furniture from the room that you can, leaving only extremely heavy furniture. Cover the floor and any remaining furniture with plastic drop cloths. Tape the edges where the ceiling meets the wall, to protect it from any stray paint.
Remove dirt and any rough areas of paint from the ceiling -- using a damp, clean cloth -- to create a smooth surface. Consider sanding the ceiling with sandpaper, to remove old paint or create an even texture on the ceiling.
Roll the paint in a “W” shape in one direction, then go back over the area to fill it in -- repeating this across the entire ceiling. Try to work quickly to complete painting it before any areas dry, to avoid dry spots or a difference in color. Go back over some of the drier sections before completing the coat of paint.