To restore an old wood dresser, clear the dresser of old paint or varnish, apply new varnish to the dresser and seal the varnish. You need sandpaper, a sponge brush, varnish, polyurethane, a screwdriver and safety goggles to complete this task.
Start by clearing the dresser of drawers and removing all knobs. Then, put on the goggles to protect your eyes, and sand away the old varnish or paint from the dresser's exterior surface with 160-grit and 240-grit sandpapers, starting with the former. Be sure to clear the surface of dust generated from sanding before and after applying the 240-grit sandpaper. Repeat the process for the drawers' outer surfaces.
Next, paint the sanded surfaces with varnish, and let the surfaces dry. Once they are dry, smooth and even the surfaces with a fine-grit sandpaper, and dust them. Sand and varnish the surfaces repeatedly, taking care to allow the varnish to dry between the coats, and stop once the surfaces are well coated and the varnish is even. Allow the last coat to dry.
Once the surfaces are dry, protect them from elements by painting them with three coats of polyurethane, allowing the surfaces to dry between the coats. Then, screw the knobs back in and insert the drawers back into the dresser to complete the process.