Bone marrow donation is surgical and requires anesthesia. They draw marrow out through your pelvic bone. Stem cell donation is like donating platelets, except that you get injections of Neupogen for a few days beforehand, to stimulate blood cell production and get stem cells into your bloodstream, so they don't have to go in surgically.
There are good descriptions of both procedures at the NMDP "Be the Match" site:
Bone marrow donation process
Stem cell donation process