It would totally depend on the state. I was married in 2007 in NY. All I had to do was (with my now-husband) go to one of the local town halls, show our ids, and sign some paperwork (to have the information down - names, the church we were marrying at, the wedding date, etc. We went for lunch, came back and hour later, and the paperwork was waiting for us - since we were not being married by a JOP, but having a church wedding.
If you are having Superman and UltraWoman exchange vows in a church, they have their own separate requirements. I was married in a Roman Catholic church and had to (with my now-husband) attend pre-martial classes (also known as pre-Canaan classes). I don't know about other faiths.
