Spit and cotton balls. If it's too dirty for that I use alcohol. Ive heard of using Murphy's Oil Soap, dilluted and straight, but understand it can remove stain pretty quickly.
+1
I know I'm a newbie, but I've had a lot of luck with saliva and either cotton balls, or a cotton/terry-cloth tea-towel. On rusticated pipes, like this old Jarl I'm working on, I use Murphy's Oil soap straight. I apply it with my finger and then wipe it off with a terry cloth after working the soap all over the bowl and stem with my index finger. This seemed to work well, and did not pick up significant amount of stain.
Yaz and I were chatting about cleaning up rim discolouring and I also use spit and tea-towels here (it keeps us in new tea-towels! :clap
and only get the sand paper out when the rim has been burned out or chewed through knocking out.
-- Pat