If you already have a marriage license, you can order a certified copy of your marriage certificate from the county clerk’s office where you were married. To get a license to marry, you have to fill out an application and pay a small fee. Some states require blood testing. In most cases you will have to go in person to show your ID and be granted the license. At your wedding, your license must be signed by all the appropriate parties, including witnesses, if required. Then the wedding officiate will send it to your county clerk’s office to be recorded before you can order a certified copy of your certificate mailed to you.
Crispy is right, each state will have their own rules. I've been married twice. Once in Georgia and once in Arizona. It was different both times. In AZ we both had to go to the clerk's office with our IDs, and our application fee, which was like $75. I brought a copy of my final divorce papers just in case they would need those, but they didn't. Just a heads up, you do need the license before you can actually have a ceremony performed. The good thing is, there's no wait. You get the license immediately so you can even get married that day (if you have someone to marry you of course!). The license expires after one year so make sure you get married within that time frame.
I think each state may have their own requirements, but I'm not entirely sure. I was married in CA. Here it's pretty simple. We both had to go to one of the local County Clerk's office in person and fill out an application, present our IDs, and pay the application fee. There was no waiting period or anything. I did find out that the license expires after 90 days, meaning you should get married within three months from the time you get the license. Hope that helps!