After you have unpinned them, knock off as much dirt and grime as possible with a rag. Find a Tupperware container that will hold them laying flat. Drop em in and cover them with neatsfoot oil. Put the cover on and let em soak for a couple of days.
After soaking, dry them off really well. Light sanding follows. I start at 500 grit and work up to 1k then 2k. All your doing is smoothing out scratches/removing a thin layer, so that the surface looks new again. I then buff the surface with white polishing compound and wipe that off with a clean rag. Last step for me is turtle wax. I'll see if I can find a sticky on restoring straights and post the link.
No on mineral oil. Neatsfoot oil is derived from cattle bones. You can find it at Wal-Mart, some hardware stores, and leather craft stores (Tandy). It replenishes the horn and keeps it from splitting or separating.