The countertops of many bathroom vanities may be made from plastic laminate, but more often it's a material called cultured marble. This is basically a mixture of polyester resin, limestone, pigments and fillers with a thin surface coating similar to the coating on a fiberglass shower or bathtub. The gel coat can sustain small scratches, and when the scratches accumulate dirt, the entire surface looks old and worn. The process for removing these scratches is similar to that for removing scratches from an auto body. You can safely remove only those scratches that don't penetrate the gel coat.
Soak a piece of 1,000-grit wet/dry sandpaper in water for five minutes or so to get it saturated.
Moisten the countertop with a sponge soaked with water, and then sand the surface with the wet/dry sandpaper. Move the paper in a swirling or circular motion. Check your progress frequently by wiping off the sanding residue with a nonabrasive cloth. If you still see scratches, wet the surface with the sponge and continue sanding.
Wipe off all the residue when you're done. Rinse the vanity with clear water, and wipe the surface dry. Spread automotive polishing compound over the surface and polish the surface with a lambswool buffer. You can buff by hand, but it's easier to use a power buffer.
Protect the gel coat with cultured marble polish, available at hardware and home supply stores. Apply the polish according to the instructions on the container.