Brass is an alloy of copper and zinc. It is generally golden in appearance and distinguished from bronze, which is copper and tin. You can typically polish brass to remove scratches. The basic technique for polishing brass is similar to polishing other metals, with the key principals being to test an area first to make sure that you don't cause undue harm to your piece, and to use a gentle touch.
Clean to remove dust and dirt from the surface. Use a clean cotton cloth and water to remove accumulated grime and a cotton swab for the details. Gently dab the surface to remove excess moisture.
Use a brass polish. Apply brass cleaner to a cloth and gently rub the cloth over the brass lamp, taking care to not be too aggressive. Test first in a hidden area that is not readily visible to make sure you do not damage the piece. In areas where it is especially scratched, buff more aggressively. Rub off excess polish, and buff the brass to a brilliant finish.
Use a rotary tool if needed to buff out deeper scratches. Use a buffing wheel and a small amount of polish and try to gently buff out the scratch.
Use a metal polish to prevent further scratches. Using a brass polish regularly will help protect the finish and prevent further scratches.
Avoid handling the clean item with unprotected hands until it is dry to prevent tarnishing.
Do not use metal brushes or steel wool, as these will damage the surface.