Purchase the proper paint. Your local paint, hardware and home improvement stores offer a wide variety of concrete floor paints -- there are several finishes and countless colors from which to choose. Don't confuse concrete floor paint with acid stain or concrete epoxy coating. These are commonly used when painting interior concrete floors, such as in garages or basements, and require a slightly different application.
Open doors and windows, and set up a fan or two, to keep the area well-ventilated.
Remove any old, chipped paint with a wire brush, if necessary. You don't need to remove all the old paint ... just the peeling bits that are sticking up.
Scrub the floor thoroughly with soap and water, rinse well and allow to dry completely. Be sure there is no loose dirt left, or the primer won't adhere properly.
Tape off edges and other areas you don't want to paint.
Apply concrete sealer/primer with a regular paint roller. Roll the primer on in a W-shaped pattern to keep a wet edge and reduce roller marks. One coat of primer is all you need, and it doesn't have to look perfect because you're going to paint over it anyway. Let the concrete primer dry for at least 1 hour, or until it has no tacky feeling when touched.
Apply the paint with a roller in the same W pattern you used with the primer. Allow to dry about 2 or 3 hours, or until it's not tacky when touched, before applying a second coat.