The most basic (but totally essential) requirement is money! You can't get a student loan for overseas study, so you'll need to find some other way to fund your course (together, of course, with your accommodation and living costs, as well as your travel). See here:
https://www.nus.org.uk/en/advice/money-and-funding/i-want-to-study-outside-the-uk--what-higher-education-funding-can-i-get/
You'll then need to find a place at a school within the US Student and Exchange Visitor Program. ('School' is used here in the US sense of the word, which embraces universities). From there you'll be able to apply for an F visa, which involves attending an interview at the US Embassy in London:
https://travel.state.gov/content/travel/en/us-visas/study/student-visa.html
You're not allowed to take up any employment at all during the first year of your studies unless it's actually on the institution's campus. Thereafter you can work off-campus but only in relation to your studies. (So don't, for example, plan on funding your studies by working part-time in a bar; you won't be allowed to).
https://www.uscis.gov/working-united-states/students-and-exchange-visitors/students-and-employment