You can drive using your US license for one year from the date you settled here. You'll need to tell your insurance company that you're driving on a foreign license. Before that year is out, you'll need to obtain a full license if you want to drive by yourself. To do this:
You'll need to apply for a provisional license -- you can get the application online or at a post office. You'll need to send in the form along with a picture, the fee, a signed referral from someone British and "professional" (other than family) who has known you for two years (or you can go to your local DVLA office and have them sign for you if you haven't lived here two years), and your passport to Swansea. You should have your passport back in a week or two and your license will follow shortly.
With your provisional license, you can drive with any UK license holder over 21 who has had their license for three years.
To obtain your full license (which will allow you to drive alone), you will need to pass a theory test and a practical driving test. There are books, websites, and cd-roms to help with the theory and hazard perception.
You might also want to take a few lessons before taking your practical exam. I personally took about 40 hours of lessons (but they were cheap because my neighbour is an instructor), but I'd never driving a manual car before (ending up buying an automatic though!
).