Melamine is a man-made substance used to laminate cabinets made of particleboard. This paper-thin chemically infused material is difficult to paint if you use the wrong type of primer. You need to clean and sand a melamine vanity before priming or painting to get the paint to adhere. Because melamine is such a slick surface, unlike wood, it requires a primer designed for plastics, laminates and similar surfaces -- otherwise the paint may peel away.
Remove the door from the vanity using a Phillips head screwdriver. Set the hardware aside in a safe place.
Cover the floor around the vanity with newspaper.
Clean the melamine surfaces, including the doors and the drawer front, if any, with a household cleaner and a damp sponge. Allow them to dry completely.
Sand all melamine surfaces with a fine-grit sanding block to scuff the finish. Scuffing makes the melamine more receptive to primer and paint. Wipe the dust away with a rag or tack cloth.
Cover all the areas you don't wish to paint with painter's tape. If the vanity has a drawer, remove it or pull it out as far as it will go.
Pour some of the primer into a paint tray. Prime all melamine surfaces using a paintbrush, allowing the primer to dry completely. If the melamine is still visible through the primer, apply a second coat and allow it to dry.
Pour some latex paint into a paint tray. Paint over all the primed areas using a paintbrush, allowing the paint to dry. Apply a second coat, if necessary.