Water and paint have an uneasy relationship. Water will wear on the paint over time and degrade the surface. This doesn't mean you can't paint a surface in constant contact with water, but you need to pay attention to the type of paint used. The additional factor, if you are thinking about painting a sink, is that not only will the sink be wet, often the water will be very hot and wet. Heat also has a strong effect on paint. Painting areas that are constantly exposed to hot water, such as tubs and showers, often exposes the weaknesses of some paint treatments.
The most common recommendation for painting over a fiberglass sink is to use an appliance paint rated for heat or a specialty paint for hot/wet environments. Begin by sanding the sink with 320-grit sandpaper until the finish is dull and hazy. Then wipe it down with a solvent recommended by the primer and paint manufacturer. When you wipe down the sink, you are removing the dust, not cleaning the sink. Often this will involve additional sanding between layers. The finish coat should be hard and as shiny as possible. Check for cure times before using the sink.
You will have much better results, when it comes to updating your fiberglass sink, by spraying the primer and paint onto the sink surface. Several companies produce appliance and hot/wet paints and primers in spray cans. Automotive paints are also an option since fiberglass is a common auto body material. You can make repairs to the sink with a fiberglass repair kit and auto body filler. This is a good idea if your sink has gouges or cracks. Do any repairs then sand the surface to a dull haze. Wipe the sink down with the solvent recommended for the primer and paint. Spray the sink with a low-pressure spray paint gun. You can rent these from most home improvement stores. This application method will give the sink a nice hard finish and increase its durability.
Gel coatings are commonly used on boats. This type of paint for fiberglass is gaining in popularity because of its known durability with water. Begin by sanding the surface to a hazy finish, then spray on the gel coat and let it dry. Sand with 100-, 220-, 600- then 1,600-grit sandpaper until the surface is smooth. Polish the sink with a rubbing compound then a finishing compound. Finally, wax and buff the surface as you would a car or boat. This produces a very durable finish that will hold up well to everyday use. Never clean your painted sink with caustic cleansers as they will eat away almost all paint treatments.