When I went to get my name change once I got married, I did not know where to start so I thought I'd help out those who have yet to get to this step.
1) Order a few certified copies of your marriage certificate (I ordered 20 and that was waaay too many...most of the places just asked to see a copy and returned it)
2) Get your updated license first. Bring a copy of your marriage certificate and if your address is changing, you'll need an actual bill with your name on it and your new address before they can make the address change to your license. Something to keep in mind- if your license happens to expire within a year, make sure to have them renew your license at the time you are getting it updated with your new name (which means you need to take the eye exam). If you don't, you'll just end up paying an additional $30 to get your license renewed in a year.
3) Take your new updated license, marriage certificate and utility bill (if your address is changing) to the social security office to get your new card (they mail it to you within 2 weeks).
4) Then on to update everything else: checks, credit cards, mortgage, insurance, employer 401K, emails, etc.
Credit card was easy- I just called them and they sent a new one...they didn't ask for any verification, but I'm sure it's different for each company.
If you want to change your middle name to your maiden name (which I originally wanted to do), call the BMV & SS office first to find out about the steps that you need to take. I tried to change it when I got my license, but I was informed (by what looked like a summer intern) that I needed to have this change reflected on my marriage license first. HOWEVER, my co-worker got it done at the BMV with no problems, so it seems the "rules" vary depending on the person you speak with. Good luck!