I have tried a number of different way to polish my pipes, and here is how I currently do it.I have tried, sometimes with good success, a "Magic Polishing Cloth", a "Magic Eraser", Briar Pipe Wipe, stem polish, olive out, etc., but ended up where I think most professionals do (what are the chances?). I purchased a ‘Two Speed 8" Bench Grinder’ from Woodcraft (http://www.woodcraft.com). Luckily, there is one here in Denver, so I didn’t have to pay shipping for a heavy object. One is interested in the slower (~1700 RPM) speed. I took the guards off (NOT usually a good idea, proceed at your own risk), found some unstitched cotton buffs, bought eight large washers as spacers so that the buffs would fit properly. I also bought some white buffing compound (fairly mild, and the only one I use) and some carnauba Wax from Woodcraft too.
Here are a view of a Wilmer Bellaire pipe with an oxidized vulcanite stem. Vulcanite stems turn white, yellow, or green with time. My understanding is that it has to do with sulfur being used during the manufacturing process.
Remove the stem from the pipe. If there is a logo, cover it with vaseline. I use a 50/50 mixture of water and bleach and soak the stem for 15 – 30 minutes. Expect some bubbling. The surface of the pipe will become white and rough. Rinse and let dry.
Important: reassemble pipe. Turn on the buffer and charge one of the buffs with the white compound. Gently and carefully polish the stem and pipe. Don’t push hard — let the buffer do the work. Keep the stem and pipe moving so that no one place gets warm. Wear eye protection. Learn with a cheap pipe — you probably will experience a couple of "fling and ding"s. Be especially careful around edges and where the stem meets the bowl — these seem to be where the buffer will catch.
Once the stem is smooth again, charge the other buff with carnauba and do more of the same. The wax will put shine on the stem and pipe and protect both. These pictures don’t really do justice to the transformation.
That’s my approach. Heed my warnings: wear eye protection, be gentle, and start with cheap pipes.