Simichrome Metal Polish
I once bought some old Dia Compe 980-R brakes on E-bay. They were made in 1983 and didn't seem to have been cleaned since then. So I poured a glass of wine, sat down in the big leather chair, and started polishing one of them with Simichrome. In about 10 minutes it looked like... Well click on the photo to enlarge it and see for yourself.
The trick is to first use a scrap of very fine sand paper, about 400-grit, to get rid of any deep scratches. Then dab a drop of Simichrome on a piece of soft cotton cloth, like an old t-shirt, and start polishing. The cloth should be about 6" x 6". Keep using the same piece over and over because the little Simi particles build up on it and make polishing even faster with use. It doesn't take long to get an amazing shine.
Simichrome polish is made in Germany and it's not easy to find. But it is the best. It does a great job on non-anodized aluminum, chrome, brass, stainless steel, and silver. It also leaves a thin film that protects the metal.
*Note: Due to VOC content, Simichrome cannot be sold in California.