As of this past summer, it was as follows:
Upon accepting you (and/or you "accepting" them), the school's international student office sends you a packet that includes some forms you fill out (mostly about citizenship and how you're going to pay for your education/living expenses in the US) and send back to them. Once you've proven to them that you won't go bankrupt once you start, they send you a form called an I-20 which is basically an invitation from them for you to come study as an international student. (This is the step for which I had to wait the longest, but it's under the control of the school, not the US government)!
If you're NOT a Canadian (I'm not sure re: UK citizens), you then take the I-20 form to your nearest US consulate and wait (in some countries this can take months and months). If you ARE a Canadian, you take this form with you, along with your passport, to the border the day you come to start school (no prior visits to the consulate are necessary). The paperwork gets done at the border in a few minutes for a nominal cost (like $6 or $12 as of last summer...). At that point, you're good to go.
One caveat - at the end of the I-20 form, there is a page where your school's representative must sign every year to keep it valid ONCE you've started school (not for the initial entry I don't think, but that might be wrong). If you leave the States and then return to school, make sure you have a signature back there that's less than a year old! I've never had a problem leaving or entering the US as long as I had my passport and the current, signed I-20 form with me (yes, one extra piece of paper to cart around...)
If you want to make sure that your paperwork is in order before starting school, the offices to call would be a) the admissions office, b) the school's international student office, and c) the US border control/customs. Tell them what you have and they should be able to fill you in.
Hope that helps!
