You'll need to get your social security card changed. You can do that at
www.ssa.gov. Just download the form, send it to the US Embassy in London w/ your passport and marriage certificate.
If you want to change the name in your passport, there's a courier service (you can find it on the Embassy's website). I'm not bothering with that until my passport expires, though. Just not worth the bother at the moment (so we book all of my tickets in my maiden name).
There's nothing to do officially over here. I just put Mrs. Married Name on everything here--bank account, credit cards, UK tax stuff, etc.
If you're working over here under your married name, you'll need to make sure you get your SS card changed so that there's a smooth paper trail with your US taxes, etc.