Wipe loose dust off the furniture using a dry cotton cloth.
Prepare to clean the furniture with mineral spirits. Open nearby windows for ventilation, and put on chemical-resistant gloves for hand protection.
Saturate another cloth with mineral spirits. Wipe the cloth over the furniture's finish, following the grain lines. Fold the cloth once it accumulates wax buildup.
Continue wiping the furniture's finish with mineral spirits until no more yellowed wax buildup remains on the finish or transfers onto the cloth.
Hang the moistened cloth outdoors to air-dry, as it is flammable. Dispose of the cloth according to local ordinances.