I can answer part of this question from the woodworker perspective; if something I advise contradicts good practice by all means I welcome a more experienced pipe person to correct me.
If you start sanding with anything more coarse than 300 grit you'l regret it. I've worked projects down to 1000 grit paper before moving on to compounds like rottenstone and such, and from what I've gathered in my research on working briar so do many of the fine pipe makers. Doing a very good job with sanding doesn't take a whole lot of skill, but it takes a lot more patience than most people have--start with 300, sand it twice as long as you think you need to with about half the pressure you think you need to, then sand it twice as long again, dust it off, then walk away. Because by then you're never going to want to sand anything again and just want the whole process to be over with. Of course sand with the grain if there is any; areas of burl call for tiny little circular motions. Much much later, after your hands have uncramped, start sanding gently again with 400 grit, then work your way through every grit up to at least 800, again spending twice as long as you think you need then doubling it. Also keep in mind that unless you have a very high-end pipe there are going to be pits and spots that are filled with putty; sanding will expose these, and using a solvent may dissolve or weaken them. Now you may need to re-fill any putty spots or dropouts that have been exposed; then some more sanding will follow but it goes faster this time. If you haven't thrown the briar in the fire or the road by now, you may consider a rubbing compound like rottenstone or the like at this point; a fine lambswool or chamois cloth dampened with saliva works best in my experience to work it in.
On the subject of coloring, unclearthur is referring to aniline dye, which actually infiltrates the wood on a cellular level, unlike stains which really only lay between and on top of wood fibers. There are two varieties, water-soluble and alcohol-soluble; for your pipe you will want the alcohol-soluble. Everclear again makes a good suspension medium for the dye; whiskey or vodka however does not. Wood alcohol, or wood spirits / wood naphtha / methyl alcohol, is preferred. You can buy dye and spirits from woodworker supply shops online. I've always warmed the alcohol slightly to ease the solution, and you'll definitely want to experiment on a piece of scrap wood to get an idea of the color. deep colors take repeated applications and / or soaking; I would also advise AGAINST exposing the interior of the bowl chamber or stem to the dye.
Aniline applications WILL bleed out their color! To get the truest color I would apply very heavily on the first application, allow to dry thoroughly, then rub in a clean cotton jersey cloth vigorously to draw out the loose color--then apply again, repeat, repeat, until I achieved the desired depth of color.
Next you'll need to seal this in, and this is where I've come across a lot of conflicting advice in my research. Personally, I would not use anything with petroleum distillates in something I was going to eat or smoke, but I've seen differing opinions on this. So from here on out, I can only tell you what *I* would do. I'd rub a seal coat in of some wood oil like tung or pine tar that was distilled with wood alcohol only, no petroleum. Then a wax coat, pure carnauba, and another and another and another until I had a glass finish.
These colors are sensitive in varying degrees to UV exposure, which is one of the reasons it's not a good idea to leave your pipe out in the sun. Red will fade quickest, then violets / oranges / yellows / blues / greens.
And this was the short version. So you can see, you can do as much or as little work on it as you want. But this is about the minimum I would do to a pipe.
Regarding stems, I've little to no experience, but I'm learning a lot from the forums and other research, and always eager to hear more.
