Spiritually speaking, what would be the best thing to do while waiting for someone to come out of surgery?
Spiritual Meditation. Occupy one's mind with meditation & prayer. Bible readings especially the miracles performed by jesus are inspiring and the promise made in romans 8:28 "... We know that all things work together for good to them that love god...." and I emphasize the word, "all." it will help make it easier to accept the results of surgery, good or not.
Pray and then read. Pray for a successful outcome and read/review about the operation focusing on what you can do to help for the patients recovery.