Does one have to make an appointment to get a marriage liscense, or can you just go sign papers?

My fiance and I have been together for years, and would like to get married as soon as possible. Can we just find a courthouse, sign papers, and be officially married? Or...would we have to call ahead, make an appointment, and wait your turn? We aren't wanting a ceremony at this time, just to get the papers signed and be legally married at this point in time. We plan to have a ceremony down the road when we can afford it. Does anyone know how things like this usually work?