My oldest graduated in 2012 from a US university, second is half way through, and third is off next week to start her big adventure. They are American though, and did high school in the US.
If you are interested, go to www.collegeboard.org/, which is an official site that can help you sort out many of the bewildering details. Your student can create an account (in fact he or she may eventually have to in order to proceed with any application).
www.fulbright.org.uk/study-in-the-usa is another site that is extremely useful.
There is a different application timetable involved compared to application to UK universities, so you will need to start looking early (now) because for admission in 2014 the application form cycle begins this autumn, with most US students having completed the necessary exams (ACT or SAT) at the latest in early summer 2013. If your student is at the end of A levels now, another year may be necessary to get the required tests done - but go through the Fulbright site with a fine tooth comb to figure out where you stand, timewise.
Once you've looked at the application schedule and know what you will need in terms of standardised tests and sending your UK school results, you need to assess where your student is most likely to be accepted and how you will manage to finance the education. Again, the Fulbright site is useful from the finance pov, and the CollegeBoard one is useful for the college search process (college = university).
American students applying for financial aid do so through the FAFSA site. Individual universities usually require an additional variety of documents for their own financial aid offices to examine. For international students, things may be different. You should be prepared to have ready a lot of documentation of income, tax forms for a few years, documentation of the value of assets, and sundry other items that individual colleges may request.
The cost of attending includes residence in a dorm and all meals. Dorms are pretty much bare bones. Rooms are furnished but you bring your own bedding, etc. The bill is usually broken down into tuition and room/board. For US students, financial aid can cover as much as 100% of need. A student could conceivably pay nothing for third level education. Students generally buy their own books and materials. You would not be forking over for private accommodation or food for your student separate from the room and board charge.
Foreign students may have a different situation, financial aid/scholarship-wise. Normally, a student applies for financial aid around the same time as the application for a place is done, but via different offices. You can't apply for aid after admission anywhere. The timetable for American students' financial aid application is end of January 2014 for admission in autumn 2014. Again, international students may have a different situation. You would have to narrow down your choices to about 6 or 7 universities and then contact each one to speak to the office of financial aid regarding your financial aid application.
American universities vary greatly in quality and rigour of courses, so it pays to do your homework, look at forums, compare university rankings, etc. and think about what your student is looking for in a university. American students applying to very selective universities would take Advanced Placement courses in most, if not all of their high school subjects in their high schools in the final two years. These are equivalent to A level courses. No student applying to a very selective university would have any hope of getting in without doing AP courses and getting a 4 or 5 (top grade is 5) on those courses.
The DCs love/d their university experience. One went to a highly selective university ranked normally in the top 10 worldwide and the other is going to a very selective state school ranked in the top 50. College life features a huge amount of action crammed into each day and night, and fairly tolerable food and communal bathrooms. Support /counselling/ health services/ academic counselling are all very good ime.
American universities generally use the gpa system that US high schools do, so all grades count towards your final grade for a course. This means students work fairly steadily (those that work). Most students hold down a part time job too. American students work hard and drink a lot of Red Bull. DS and I had a few interesting conversations last year at the point where he had been up for three days and nights straight, finishing up papers and studying.
While there are usually general education requirements (maths, humanities, foreign language, science, English, etc), sometimes called a Core curriculum, most students are taking lots of courses in their focus area by their second year even though you don't have to declare a major until your second last year.
Students generally take four or five subjects per semester. As an example, DS's subjects last year included maths courses, chemistry, chem lab and organic chemistry, biology (2 different courses plus labs) a course on history of film. This coming year he will be taking physics and more bio and chem and maths (stats and calc 3). He has almost finished his gen ed requirements and will be left with Latin to take in his last year. He is on track to go to medical school. DD1 at one point was taking visual arts courses, psychology, philosophy, Persian, French, physics, calc 3, and various economics courses (her major was econ with a minor in visual arts).