What are the requirements of an American student in getting into Oxford?
The same as for any student to get into Oxford- just substitute a 5 on relevant APs (or strong 700s on subject tests) for “A at A-level” . There is a huge amount of very detailed information on the Oxford website, and I strongly encourage you to spend a lot of time there. They also have podcasts on iTunes and vlogs on YouTube which are helpful.
The short answer is a minimum of 2100 on the SAT + 3 APs in subjects that are relevant to the subject you are applying to study (some subjects may be specified, ie for econ you need math)*. Depending on the subject there may also be an aptitude test, and of course an essay and recommendations (ECs are only considered if they relate directly to your subject). If you those pieces are strong enough, you are invited to have an in-depth interview about the subject with the college tutors (professors), which is when the final decision is made (either at Oxford, or by Skype).
*you apply to study one (or 2 pre-combined) subject(s), and that is all you study. Look up the subject(s) you are interested in and you will find very detailed descriptions, right down to the classes required each year of your degree.