Sand the polyurethane surface with 220-grit sandpaper attached to an orbital sander. Allow the weight of the sander to press onto the surface of the desk to prevent the removal of the entire top coat of polyurethane or damage to the stained surface.
Wipe the surface clean with a damp cotton rag. Sand the damp surface with 320-grit sandpaper, applying light pressure. Wipe the dust form the surface of the desk and observe whether the scratch still remains. Continue to sand until the scratch disappears.
Wipe the desk top clean with a damp rag and dry the desk completely before proceeding. Wipe the surface in circular motions as if you were polishing the finish. Remove lint and threads with a hair dryer to prevent any contamination of the new finish.
Wipe on three coats of polyurethane gloss or satin clear coat, allowing 30 minutes to one hour drying time between coats. Wipe the polyurethane on rather than brushing. This will create a smoother appearance because each coat is applied in thinner applications. Rub each coat with #0000 steel wool prior to applying the next coat.
Allow the polyurethane to dry and wipe on paste wax with a cotton rag. Apply the wax in the same manner as you would car wax. Allow the wax to set for 10 to 15 minutes and wipe away with a clean cotton rag.