The American University System if very varied.
There are Public Universities, Private Universities, Technical Colleges, Liberal Arts Colleges, Conservatories. Lots of different options.
Community Colleges, they tend to be very, very, very cheap. Chabot College charges $36 a unit, so you might pay $108 for a class. If you are going full time, you probably spending $432 a semester. Community colleges tend to not have 4 year+ degrees, however. They tend to have 2 year degrees. So people will often go to a community college and then transfer to a bigger college. Community colleges also tend to be "commuter colleges"--so there are no residence halls, you aren't living on campus, they don't have the same sort of extra-curriculars.
Public Universities. They are run by and subsidized by individual states. The University of California, Los Angeles, Or Ohio State University. These schools can get really large. UCLA had 50,000 people running around on campus, for example. These schools tend to have a full range of degrees: Bachelors of Arts, Bachelors of Science, Masters Degrees, PhDs. Some of them have Law Schools, Medical Schools, Dental Schools, or Engineering Schools attached. These schools tend to be not as expensive if you are a state resident, expensive if you are an out of state resident. UT Austin's costs:
Texas resident on-campus $23,596 ? 24,936
Texas resident off-campus $23,734 ? 25,074
Non-resident on-campus $35,776 ? 45,960
Non-resident off-campus $35,914 ? 46,098
Big Public Universities are like private Universities in that they tend to offer big and varied experiences: Sports Teams, School Newspapers, Literary Journals, Orchestras, clubs, etc.
Private Universities, like Harvard, Princeton, Yale. Tend to be expensive. Harvard's Tuition is $33,696 and the total cost with fees, room, and board was $48,868. A place like Harvard has a lot of resources, the full college experience, Professors who are leaders in their field, and they actually aren't that big. They have around 7,000 undergraduates and 14,000 post graduates.
Small Liberal Arts Universities tend to be expensive and really small. They may not have all the sports teams or extra-curriculars...they probably also won't have the research labs of a big University. They also, often don't have graduate degrees. But the education they offer tends to be really, really amazing. I went to Mills College. A women's only college in Oakland with an enrollment of around 700 undergraduates. Liberal Arts colleges also tend to end up being $50,000 a year with room and board.
Those tend to be the four big categories. There are other things like a conservatory where you go to get a Bachelor's in Music and just play Music with minimal academics. There are technical colleges where you do minimal academics, but go to learn to be a Mechanic or Paralegal or something like that.
Note about cost: US Universities are expensive on the face of it, but those don't tend to be what people actually end up paying. We have extensive financial aid, and there are lots of scholarships. Big, rich private universities also tend to give lots of scholarships as well. If you are a person without a lot of money, you can often leave your institution only having paid a small fraction of the total cost.
For example, Mills College, where I went for my undergrad cost $51,547 a year (including room and board). I don't have that sort of money to be sure. But I got Pell Grants (grants from the federal government), Cal Grants (grants from the California state government), I got scholarships from Mills College itself, I also had the GI Bill (money paid by the government for people who had served in the military). I paid for some of the bill myself through student loans. So, how much did I pay total for four years at that pricey school? $11,000...or $2,750 a year. It is something similar at places like Harvard, Princeton, and Yale. So while the price tags look high, that is often deceptive.
You tend not to have to pay for PhDs if you get admitted to a top-rated university.
Applications:
In the US you apply to individual schools. Many of the schools want similar things (High School Transcripts, SAT/ACT exam score, sometimes personal statements, sometimes essays or writing samples, sometimes resumes). But each school is different, and they all have slightly different requirements.
And one of the big differences between British and American (US) universities:
In Britain you apply into a major. So you apply to study German or History (or whatever). If you end up going to the University of Liverpool for History, and after a year you decide you'd rather do German Studies...well you have to reapply to University. That isn't how US undergraduate institutions generally work (there are exceptions for Schools of Engineering or Conservatories). In the US you apply to the institution in general. While you might indicate a major interest, you don't apply to a major. When you come into the University, you don't have a major declared. Most Universities and Liberal Arts Colleges require you to take between 8-10 courses across different disciplines (general education or distribution requirements) in order to make you a well rounded scholar and to give you access to different kinds of thinking. Students then usually declare their major (or double major or major/minor) in their second year of college. Though, some declare in their first year, because they know what they want. Others might declare in their second year...and then change their mind and declare something different in their third year.
Of course, graduate school--Masters or PhD's--you apply for a specific major and don't tend to take (m)any courses out of your major. But that is a different situation.
Hope that helps some. I'm a University Professor, so I can give further insights if you have specific questions.
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