Remove the drawers from the dresser and take off the hardware such as handles or knobs. Wash the drawers and dresser frame down with soapy water. Use a toothbrush to clean stubborn areas such as trim.
Strip off the old paint from both the dresser and drawers. Follow the directions on the paint stripper for proper application. You may need to use a paste stripper on raised areas.
Sand the wood to remove imperfections. Wipe the surface down with a wet cloth to clean it after sanding. Run your hand over the wood, feeling for bumps or raised areas. Focus your sanding on these spots to smooth out the surface.
Apply a thin coat of oil-based paint to the dresser frame and drawer fronts. Follow the directions provided with the product for proper application. Let the paint dry halfway. You want the paint to be slightly wet when you apply the top coat.
Add a thin layer of water-based varnish. The top coat will dry faster than the bottom. This will cause the finish to crack naturally. Let the dresser and drawers sit for several days so both layers of paint dry completely.
Rub on a layer of paste wax onto the dresser and drawers. Follow the directions on the product for application. Work the wax into any cracks that form in the paint. This will seal the paint and protect the wood underneath.
Install the hardware on the drawers before inserting them back into the dresser frame.