How to efficiently paint a ceiling.
Use a 3 or 4" brush to paint a strip around the edge of the ceiling. Divide the ceiling up in your mind into 6 - 8 foot blocks (i.e. a 12-16 foot wide room is 2 blocks). Load your roller and apply paint to first block, in a strip no more than two feet wide. Do a series of W's rather than straight lines. Do a couple of strips, then with little or no paint on the roller, lightly roll from the wet edge into the dry edge in straight lines. Repeat until finished.