Dust the surface of the furniture with a soft dusting rag or feather duster to remove fine particulates that could further scratch and dull the finish.
Apply a small amount of odorless mineral spirits to a soft, lint-free cloth. Rub the mineral spirits onto the surface of the furniture, frequently adding more and using a clean piece of the cloth each time as the wax breaks up.
Continue rubbing mineral spirits into the wax and buffing it off with clean rags until the entire piece has had a general once over. Go back into stubborn and detail areas with mineral spirits and quad zero steel wool to remove the waxy build-up. Work with the grain, applying only slight pressure. Replace the steel wool as needed to prevent reapplying the wax that comes up in the steel wool.
Sand the furniture surface lightly with emery cloth. Work with the grain and avoid staying in one place too long to prevent wearing through the color coat of the finish on your furniture.
Apply a new coat of Trewax Hardwood Floor Refinisher or Paste Wax to restore the shine. Use a soft sponge or lint-free rag and follow the label instructions for best results. For refinisher, simply spread and leave the finish on the surface to dry. For Paste wax, apply the wax, allow it to set until it becomes hazy, then buff it to a clear shine.