Wipe the furniture with a clean soft cloth to dry-dust the piece and remove any small particles.
Mix trisodium phosphate with water according to package directions. Choose the most diluted mixture possible to prevent the TSP from damaging the wood.
Put a small amount of TSP on a soft rag and begin gently rubbing it into the furniture. The dirt and any wax buildup will begin lifting from the furniture. Rub the furniture with the rag until one part of the rag is soiled. Rotate the rag to find a clean spot to avoid putting the dirt back onto the furniture.
Dip a soft-bristled toothbrush into the solution. Gently scrub any crevices to remove dirt in these areas. Wrap a toothpick in a soft cloth and slide it into the crevice to work the dirt out.
Rub the bare wood gently with 0000 steel wool. Do not apply firm pressure. Press lightly to avoid scratching the wood.
Dip a clean rag into paste wax and apply a thin coat of the wax to the surface of the antique. Do not use polyurethane on an antique. Rub the wax in completely, protecting the entire surface.