For the briar, you can't go wrong with ascending grades of micromesh (think ultra-fine grit sandpaper used in automotive finishing) to bring back the luster. If you have access to a buffing wheel, a block of carnuba will also serve you well, if not you can find pastes made of a mixture of carnuba, beeswax and microcrystaline wax which can be applied by hand (look for Salad Bowl Polish). If you want to strip the stain (to either leave in natural, or to restain), simply submerge it in a bath of 90%(+) isopropyl alcohol then lightly sand (repeat as needed). To restain, find a cobbler and buy some leather dye.
As for the metal portions, I can't claim to have much experience restoring metal pipes, however I would turn to pipe-cleaners and high-proof alcohol (or 90%+ iso) to remove any gunk inside. The exterior would get hit with a metal polish.
The stem/bit could require steaming to remove dents (if the surface isn't cut), or possibly even a fill or two for deep bite marks. Steaming is pretty simple, cover the dent with a wet cloth and hold a soldering iron tip against it for a couple of seconds. For fills, I use a mixture of vulcanite dust and crazy-glue mixed into a putty. Around the button, needle-files or dental tools can come in handy to clean out the old mung trapped against the button. To finish it off, I use ascending grades of micromesh, or hit it with a couple of different abrasives (jewelers rouge, white diamond, etc.) on a buffing wheel before applying carnuba. Also, if you order anything from the U.S. etailers, get a bottle of Obsidian stem treatment with your next delivery - it's cheap like dirt and will last you ages while protecting your vulcanite.
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