Repair scratches in polyurethane by testing to identify the finish, sanding the surface, removing the sanding dust and applying enough coats of new polyurethane to level the surface again. Fill any nail holes or gouges with a sandable wood filler before making the repairs.
If the wood finish includes paste wax, remove it with mineral spirits before proceeding. Lacquer, shellac and polyurethane all create similar looking finishes. Before making any repair, test the surface in an inconspicuous spot to identify the finish. Test for shellac with denatured alcohol and lacquer with lacquer thinner by dipping a cotton ball into the solvent and applying to the selected spot. If neither solvent softens the finish, it is polyurethane.
Use fine sandpaper to lightly sand the surface until the scratches disappear. Use a tack cloth or slightly damp rag to remove any dust from sanding. Apply the polyurethane using an artist brush by dipping the brush into the finishing material, tapping away any excess with a paper towel and applying the material. Allow the finish to dry 24 hours between the first and second coats. For any subsequent coats the surface should be dry, but you do not need to wait a full 24 hours before continuing.