Getting a marriage license is pretty easy. Here's what I remember us doing (keeping in mind that the process may be a little different state to state):
1. Both of us went to the county offices (if you don't know exactly where to go, just Google your county's government building and then call them up and ask specifically where to go and what to bring with you)
2. We both filled out paperwork - this just verified our names, social security numbers and that we were applying to marry each other.
3. About three business days later my fiancé ran into the government building and picked up the marriage license. It was good for 30 days so we have a full month to get married before it expired.
I think in total, the cost of the marriage license was no more than $30.00