Arrange sheets of newspaper below the paneling by putting the sheets of paper on the floor and pressing against the paneling. Tape the newspaper to the floor with pieces of masking tape. Cover the ceiling or wall above the paneling with more paper and tape.
Dust off any dirt or debris from the wood with a soft cloth. While wearing rubber gloves and a respirator or mask, apply a thin layer of paint stripper to the wood. Apply the stripper to a manageable area, because it dries quickly on the wood.
Scrape off the old stain from the wood paneling with a putty knife. Work your way around the paneling, applying more stripper to another small area and scraping off the old stain. Sand off any remaining stain with fine-grit sandpaper.
Repair gouges and other damage with wood putty. Press the putty against the damaged area and run the putty knife across the top, scraping off any excess putty. Once the putty dries, lightly sand the surface with sandpaper, making the putty even with the wood.
Rub the new wood stain on the paneling with an old rag, following the grain of the wood. Let the stain sit for a few minutes, then use a second rag to wipe off any stain the wood has not absorbed. If you want a second coat of stain, lightly sand the wood before applying the next coat.