Saturate a scrubbing pad with rubbing alcohol. Shellac can be dissolved with alcohol. Take a cloth and fold it several times to make a pad, and then dip the entire pad into the alcohol. You can leave it sitting to fully saturate the pad.
Rub the pad over the shellacked finish in a circular motion. Start at the edge of the piece and slowly rub the alcohol into the finish. This will only remove the shellac, not the actual wood stain. The shellac will appear to dissolve and streak as you do this. If necessary, repeat the process to further loosen the shellac.
Using a scraper, gently remove the remaining shellac from the wood. The alcohol should make the shellac turn into a jelly-like mixture. Gently scrape it off the surface, taking care not to gouge the wood as you work.
Rub the piece with alcohol one more time. This will remove any small pieces of shellac that may still be present on the furniture. Give the piece time to dry before proceeding.
Reapply the shellac or polyurethane. Some stores still stock shellac, although it is getting hard to find. If you cannot find shellac, you can use a clear polyurethane to recoat the wood. Use a paintbrush, and work with the grain of the wood to apply the first coat. Do not over-apply either shellac or polyurethane. For a simple covering, one coat will do. If you want a high-gloss finish, add two to three coats, giving each coat at least six to eight hours to dry.