Wash your vanity thoroughly with soap and warm water and let it dry thoroughly.
Sand the surface of your vanity to rough it up and promote paint adhesion. Sand a little deeper on corners and edges to make them more rounded, like antique furniture would be. Wipe away sanding debris with a damp cloth.
Paint your vanity with a cream-colored base coat of paint. If you're painting over a dark color or want more coverage, apply a second cream base coat. Don't let the paint dry; just let it sit for a couple of minutes.
Paint on your black paint while the base coat is still wet. Paint strategically, working in small areas at a time; paint lighter coats where the piece would have endured a lot of wear (e.g., the top, areas around the handles and any other areas you would touch regularly when using the vanity). Paint darker coats in spots that wouldn't be touched often.
Carefully drag a clean rag over the surface while still wet to blend the top and base coats, to approximate the effects of paint wear over the years. Let the paint dry.
Run a steel wool pad over some edges of the vanity to wear down to the base coat or underlying wood. Don't do this evenly over all the edges; only select strategic areas to approximate the effects of rubbing, bumping and erosion over the years.
Mix mineral spirits with black paint to make a wash. Apply wash to your vanity, working in small areas at a time. After 5 minutes, wipe the wash away with a clean rag. Work wash into any cracks, pits and crevices to create an effect of dirt accumulating over the years. Wait for your vanity to dry completely.
Apply furniture wax to your vanity with a soft cloth to give it a shiny, protective finish.