Apply a heavy coat of chemical stripper onto the patio furniture with a paintbrush. Allow the stripper to sit on the furniture for the amount of time recommended by the manufacturer.
Use a putty knife to scrape off the old finish from the furniture. Work slowly to avoid gouging the wood. Scrub the old finish with steel wool in hard-to-reach areas like chair legs.
Wipe the patio furniture down with a cloth and paint thinner to remove traces of the chemical stripper. Allow the furniture to completely dry.
Sand the patio furniture by hand with 120-grit sandpaper. Sand the entire piece to remove the remaining bits of old finish and marks in the furniture. Wipe the piece with a tack cloth to clean off sawdust. Sand the furniture again with 220-grit sandpaper to completely smooth the wood. Wipe again with a tack cloth.
Brush a thick coat of sanding sealer onto the patio furniture and allow it to soak into the wood for a few minutes, then wipe off excess with a clean cloth. This will prime the wood for the new finish. Allow it to dry and lightly sand the piece again with 220-grit sandpaper.
Brush a coat of stain onto the patio furniture and allow it to soak into the wood for a few minutes. Wipe off excess stain with a clean rag. Allow the stain to dry.
Brush a thin coat of polyurethane onto the patio furniture with a brush in long, even strokes. Avoid creating bubbles in the polyurethane. Sand the furniture with 220-grit sandpaper and apply a second thin coat of polyurethane. This will seal the patio furniture and protect it from moisture.