Remove the screws from the dresser hinges if the dresser has doors and remove the doors from the unit.
Pull out the drawers from dresser. Remove all the hardware from the drawers and the door using a screwdriver.
Apply a denatured alcohol to the surface of the dresser to test the finish. If the finish comes off, it is a shellac; if it comes off partially, it is a polyurethane stain. If it doesn't come off at all, it is an oil stain. Use this information to find the correct chemical stripper for the finish on your dresser.
Rub the stain remover onto the surface of the dresser using a rag.
Scrape the finish off the dresser surface using a paint scraper. Use a piece of 220-grit sandpaper to remove stain from hard-to-reach nooks and crannies.
Fill any large dents in the dresser with wood putty and allow the putty to dry for 24 hours. Sand down the wood putty and remove the dust with a clean rag.
Dip a rag in shellac and rub it onto the surface of the bare wood. Allow it to dry for 24 hours.
Apply a color stain of your choice to the dresser using a 2- to 3-inch paintbrush. Use a detail brush for the hard-to-reach areas. Allow the stain to dry.
Attach the new hardware to the dresser using a screwdriver.