How does an American get in to a program like this? Especially if, say hypothetically, they dropped out of school to work.
The application process is phenomenally simple, especially when compared to that for American universities.
1. You fill out an application for Oxford, containing basic biographical information and some information about the course and college you want to apply for.
2. You fill out a more detailed UCAS application, with your academic history, etc. and write a personal statement
3. You get called for interview either by phone, in person in New York/Vancouver, or in person in Oxford depending on what you can do.
4. You take an exam in your subject of choice.
All of this happens between October and November, and you get a response in late December.
Your choice of College is somewhat important, as it determines the life you'll have at Oxford, so research that in some depth. I went to New, and loved it, and my thesis supervisor was at Magdalen which is just lovely in every conceivable way (he's also a pretty kickass Computer Scientist).
Academically, you'll want a decent SAT score, a good mix of SAT II's and AP's, and a good recommendation from a teacher in a relevant subject area.