Remove the doors and hinges from the cabinet base to clean the doors and base separately. Lift out the shelves from the base. Lay the doors flat and place the shelves on top of a cloth on a clean counter or table. Remove the hinges and knobs or handles and set them aside.
Dampen a soft cloth or a synthetic steel wool pad with mineral spirits.
Wipe the cabinet surfaces, including the doors, shelves and all sides of the base, with the cloth two or three times to remove the residue. Use a new cloth or pad when it starts to look dirty. Continue to wipe the wood until the cloth or pad remains clean after wiping the surface.
Wipe the cabinets after sanding with a dry cloth to remove any remaining dust.