How do atheist weddings work?

Well I'm not getting married right now, but I am curious since I will be the first in my family to break from the church tradition. I know the justice of the peace does it, but how far will he, if he, travels to a wedding and what things are said including the vows and such, and if they aren't personal does religion have to be requested to not be included or what? I'm confused. Any help on pleasing those who are very religious in your family who will be attending would help too.