Good advice so far...when I came over I had to book a significant number of lessons even though I had been driving in the US for years (I think it took me a bit longer because I never had driven a manual car before and wanted to pass the manual test. If you sit the test in an automatic car, you are only allowed to drive automatics).
Unfortunately, you can't just convert a US driving license into a UK licence (some other countries allow conversions, I think Germany might be one. Other countries [mostly commonwealth ones] can swap their licence for a UK one but not the USA), so as folk have said, once the year is up or the US licence expires, you need to take a road test. I used to think the 'clock' resat every time you left the country, but it's when you first move here and I think there are a few documented cases where people were found to be driving illegally or their insurance wasn't valid when they had an accident because they had been using a US licence for a long time.
The first thing I did was apply for the Provisional licence (a learner's permit sort of). I found the DVLA much easier to deal with than the DMV. I did everything online and only saw a person when I went to their office to turn in the application as they had to sign my photo or something like that. I didn't wait very long either and they were pretty friendly. You can do most things online or by post, I had to send in my US passport but it was returned pretty quickly.
I think it would be good to book at least a handful of lessons before sitting your test and see how you and your instructor feel. You have to pass a Theory Test which incorporates questions and a 'hazard perception' bit, this test was taken on a computer. 'The Highway Code' is the resource book to have, and I'd recommend one of the driving-test CD-ROM's. I found it really helpful and actually the CD was more difficult than the actual test, which boosted my confidence. After you pass the theory test, you can then book the practical test.
The practical test you can research online, it's usually 40 minutes to just around one hour and involves different maneouvers, road types, and hazards. It is much more difficult than the US test, I passed on my 4th try, but many pass first time around...I just was nervous and made silly errors.
I found my insurance was soooo much cheaper with a UK licence than a US one, so you may save money in the long run. The tests are quite expensive (I sat mine a few years ago, think the theory was around £28 and practical was £37 and provisional licence had a fee too, plus lessons were £17/hr, not sure what they're like today but you can shop around for a deal). In the long run, I found it to be totally worth it and now need a car for my job as I live in a rural area.
You do keep your US licence as it's not actually a swap in this case
. Just remember to renew it!