Firstly you need a paint that covers well and has a good spreading rate. See Interior and Exterior Paints
The best and fastest way to paint a ceiling is if you have two people (do try your best not to be one of them!) You need a team of two because one paints with a brush from the wall to the ceiling, also called cutting, and the other person paints the rest of the ceiling using a roller. Lap marks result if the cut-in paint dries before you blend in the rolled area with the cut-in area, so try and work together, because the textures that a brush and roller leave are quite different.
Pro Tip: Before you use a new roller, wrap it with duct tape and then peel off the tape. This will get rid of all the loose fluff preventing any of it sticking in your paint on your beautifully painted ceiling.
If all else fails, of course, call the experts. We have a variety of Skimming Products that will make your handyman life a lot easier.