I cannot improve on this treatise of restoring a pipe at home, except nothing is mentioned of how to put the gleam back to the pipe after deep cleaning.
After deep cleaning, you’ll need to rub in as many applications of grape seed oil as the briar will absorb, using a paper towel, let dry, and buff with a wool rag or old wool sock.
I used to use olive oil for this, but on this forum I learned that grape seed oil is better, because it doesn’t go rancid and I don’t think it darkens the briar as much. An 8 ounce bottle will last for years.
ORGANIC GRAPESEED OIL, COLD PRESSED. Ingredients: Grapeseed oil, 100% Pure with NO additives or carriers added. It is noted to be especially effective to help the skin around the eyes. It's commonly used in stretch mark preparations.
www.ebay.com
Mineral oil will polish the vulcanite stems, but I only use Obsidian Oil now. Other cleaning potions will work on vulcanite but I like this best, and declare it magical how well it works.
Obsidian Pipe Stem Oil isn’t a wax or a cleaner. Obsidian Pipe Stem Oil is specifically designed to help keep your vulcanite, ebonite or cumberland stems from oxidizing, and help keep them looking newer for longer.
www.ebay.com
After you’ve gone to all the trouble to restore your pipe, in the future I recommend using 190 proof Everclear and pipe cleaners and paper towels to keep it fresh.
A bit of prevention saves hours of curing neglect.