Hi! I'm in the Tampa Bay area too! It was very easy. I downloaded the form on-line from the SS website (just search "name change" in the form search box). Take the form, your current SS card, and your official marriage certificate to the local SS Admin office. Make sure you double check what the clerk types because she messed up my middle name the first time. I honestly cannot remember if she gave me my new card right then or if it was mailed to me? I think she gave it to me right there, but it's been almost 3 years and I don't remember. But I know I still have my old SS card.
Once you have your SS card it's easy to change your driver's license. Take your SS card and your current DL to any DL office and they'll walk you through the process. I think I brought the marriage license to the DL office too but I don't think they needed it, just the SS card.
Your bank, credit cards, passport, etc. will want copies of your marriage license and possibly your new SS card or DL. I did the credit cards via fax and one took it over the phone with no proof!
Don't buy one of those "change your name kits" they are a total waste of money! It's very easy to do, it's fast, and it's free (The DL might have cost something but mine was up for renewal anyway, so that might have been why I had to pay?). I think it took 2 days total and that was because I couldn't do SS and DL the same day.