Sand over any rough spots on the interior and exterior of the tub with steel wool. You will need an even finish for the new paint.
Fill in scratches and dings with fiberglass putty using a putty knife. Smooth on the putty, scrape off the excess. Let it dry for at least 12 hours before sanding it smooth.
Open up the windows in the bathroom for better ventilation. The type of paint you will be using is noxious.
Place dropcloths around the tub and over any fixtures. This will prevent over-spray from ruining your fixtures or anything else in your bathroom you don't want painted.
Prime the tub with epoxy primer. The primer is thick and will need to be applied with a paint brush, not a sprayer.
Paint the tub with white acrylic urethane paint and a cup sprayer. This paint provides a hard and shiny finish once it cures. The cup sprayer will give you even coverage. Paint at least two coats on tub, wait about five to 10 minutes between coats. Let the paint cure completely, according to manufacturer directions, before using the tub. Approximate curing times range between 24 and 48 hours.
Polish the surface with an automotive polishing cloth to give it a nice shine.