1. Book a wedding time with the officiant of your choice - local judge, priest/pastor, justice of the peace, etc.
2. Go to county/city hall and pruchase a marriage license in accordance with your state's laws. Some states allow you to get married the same day you get the license and some require a 3 day waiting period. Most states' licenses expire after 90 days, and if not married by then, you have to get a new one.
3. Do any pre-marriage counseling required by your officiant.
4. Get married. Either you or the officiant takes the signed marriage license back to the county/city hall to get your marriage certificate. Some places give you one certified copy for free and you pay for any additional copies. Some make you pay even for the first one. I suggest you get 2 copies - one for her to keep somewhere, and one for you to keep somewhere else.
4. Take copies to the Social Security office, DMV, your insurance companies, banks, credit cards and any other accounts she wants to change her name on. For the SS office, DMV, and most banks, she will have to appear in person. Most other places will either take her word for it or just need a copy of the certificate mailed in. The DMV will probably also require her to bring her birth certificate, so she should lug that around with her for a while while she's changing everything.