What is the best way to paint popcorn ceilings?

Prepare the popcorn ceiling by gently vacuuming it. Take care to remove the dirt and dust that clings to the ceiling in front of air conditioning registers.  
After a good cleaning, you may even decide that you no longer need to paint.
But if your ceiling does need painting, mask off the room with low-adhesive blue painter’s tape  and Visqueen plastic, taped right at the top of the popcorn ceiling where the wall meets it. Rent an airless sprayer from any rental yard (have them demonstrate the use of the machine) and apply two good coats of paint in any color. There is no good, clean way to roll paint on a popcorn ceiling.