The VERY most important thing in working with gunstocks, especially older stocks, is to be patient with the processes. The more you get in a hurry to get it done, the more mistakes YOU WILL MAKE. Believe me, I know :)
I like to keep things as original as possible, but will give you three ways to clean/refurbish your stock.
For most stocks a simple wipe with a rag and your favorite solvent (mineral spirits or turpentine) will get most of the "dirt" and grime off the stock. This is the least intrusive on the original finish. If more is needed ....
An Oil Scrub: Mix a 50/50 solution of Boiled Linseed Oil and Turpentine (mineral spirits is fine) and with a #00 or finer buffing pad (I no longer use steel wool), scrub it into the stock. A light rub is usually sufficient. When you've scrubbed the entire stock let it set for about 20 minutes. Then with a terry cloth type towel or rag, wipe the stock clean. After letting the stock set for a minimum of 24 hours you may repeat if desired. The stock is ready for the next step if when you wipe your hand across it, your hand doesn't glisten. If it glistens even a bit - give it some more time before the next step. If I do oil scrubs, I usually do two before I do anything else. In rare cases ...
Refinishing the stock: Use a good wood striper only and follow the instructions to strip the existing finish off the stock. You may have to strip the stock more than once before you get all the existing finish off. I've rarely been able to get it all off in one attempt. Also, use those big heavy rubber cleaning gloves when you do - just take my word for it.
If you happen to have a Russian rifle that has a shellac finish on your stock everything is pretty much the same until you get to refinishing it. In order to strip the stock you will need Denatured Alcohol, buffing pads, several rags and patience. The Denatured Alcohol will cut the shellac and then you basically wipe it off. Do small sections at a time and be patient - you'll be able to clearly tell when you have clean wood. You may or may not want to use a wood stripper afterwards. It does tend to help.