Remove the old dresser drawers, and use a screwdriver to remove the existing drawer knobs or handles.
Repair dents and scratches. Purchase wood filler from the hardware store. Apply filler to your finger or a putty knife and spread it over scratches and dents on the dresser's surface.
Use medium-grit sandpaper or an electric sander and gently glide over areas containing the wood filler. This evens out any bumpiness caused by the wood filler and creates a smooth surface.
Sand the entire dresser and drawers with an electric sander, if you prefer a wood stain finish.
Prepare the dresser and drawers for painting by applying one or two coats of primer. You can apply primer to metal or wood surfaces, and this substance helps paint adhere to the dresser.
Add a fresh coat of paint or wood stain. After sanding the dresser and drawers, or after the primer dries, use a paintbrush to apply a coat of paint or stain. Allow the paint or stain to dry overnight, and then apply a second coat.
Install new hardware. Once the paint or stain dries, attach new handles and knobs to the dresser drawers. Use the existing holes, or drill new holes if you filled the previous holes with wood filler.