Polish a headlight lens by gently washing the lens with soap, masking the borders off with tape, sanding the surface, and rubbing in polishing compound. After thoroughly rubbing in the polished compound, rinse the headlight.
Was the headlight lens before polishing, and if it's a more heavily obscured lens, sand it first. If the lens is very heavily worn, you may need to sand it multiple times, with progressively finer grades of abrasive. Neglecting to sand worn headlights results in a rougher, less glossy surface. The abrasives work to remove irregularities that keep the lens from shining as brightly as it should. While you can buy all the supplies for polishing separately, many automotive hardware stores sell kits that include sandpaper and polisher.