Clean the aluminum item thoroughly with dish soap and hot water. Rinse the item and dry it with a towel. Do not place aluminum cookware in the dishwasher as the heat of the water and the dishwasher detergent may cause more damage.
Rub the scratch with fine sandpaper in a circular motion or in the direction of the grain. You can also use fine steel wool or wet-and-dry sandpaper. Do not rub too hard or you will make a noticeable smooth patch in the aluminum.
Wash and dry the aluminum again, using dish soap and hot water for cookware or an all-purpose cleaner for aluminum wheels or other items. Use a microfiber cloth to dry non-cookware items.
Buff and polish the aluminum with a high-quality polish. Follow the manufacturer's instructions. Some polishes are applied by hand, while others require a buffing tool. Alternatively, take the item to a machine shop that offers buffing services. Buffing is optional, depending on the aluminum item and how deep the scratch is. It's generally not necessary for aluminum cookware.