Remove the drawers from the dresser, and unscrew the handles or knobs.
Pour paint stripper in an aluminum tray.
Use a paintbrush to apply stripper to the entire dresser. Allow it to sit as instructed on the container.
Scrape the old paint off with a putty knife. Repeat the stripping process if all the paint does not come off the first time, which happens with thicker coats of paint. Don't forget to strip the front of the drawers, too.
Fill in any holes or cracks with wood sealer.
Sand the surfaces of the dresser. You can use an electric sander or sanding sponge to make it easier to cover all surfaces. Sand any surface you plan to paint, then wipe down the surface with a cloth.
Apply a coat of primer to the dresser. Use a paintbrush to spread it on the dresser in short, even strokes. Allow it to dry as instructed on the label of the primer.
Paint the first coat of paint on the dresser, and let it dry. If necessary, apply a second coat after the first one dries.
Reattach the knobs or handles to the drawers after the paint is completely dry.