OK, you've made your short list. You know roughly which unis are sure things, which are fall-backs and which are a definite stretch. Now what?
Step by step, here's what to do:
First, contact each university directly or go to their website to obtain information and application materials.
Most of them use will the 'Common Application Form' (see www.commonapp.org), which allows you to complete one application online and send it electronically to all the schools you are interested in.
However, unlike UCAS, even if you use the Common App and fill it out only once, you will be required to submit it to each university individually (usually with the school's own supplemental application) and pay a fee to each one (currently about $75).
The Common Application (& Essay)
The Common App will ask you for personal data, grades etc - but the biggest challenge will likely be the personal essay. You are given several choices for topics, so there is usually plenty of flexibility, and you only have to choose one of them.
These essays tend to be in response to a vaguely worded question about your values, your interests or your most significant experiences and while the whole thing may seem a bit pretentious, its importance should NOT be underestimated.
In your essay, make sure you reveal things that are unique, interesting and informative about yourself. Pick something you’re interested in – the essay will read much better if you have some conviction when you’re writing it.
Be aware - this is a key part of your application so think about it carefully and bring out your best writing skills. (And make sure other people read it through for typos, grammar and other suggestions before you send it off.)
Supplemental uni essays...
In addition to the Common Application, many universities also have a Supplemental Application with questions about your specific interest in their school and your qualifications - often requiring short essays in response. (Unlike the UCAS form, where you do not discuss individual institutions, US universities will want to know why you want to attend their school in particular.)
Americans tend not to be reticent about their personal achievements, so don't hold back out of any false or British modesty. Make sure your prospective university really knows about how wonderful you are, how much you want to attend their school, and what a great addition you will be to their student body.
It is crucial you take your time over these Supplemental Application essays, as they are often the deciding factor in admission. Each university is trying to suss out if you will fit in: if the hard data (test scores/grades) are not quite at the required standard, or if the competition is hot, your essay could sway the decision. Again, each college will be looking for candidates that suit them, so remember to target each essay individually.
There are many organizations, such as EducationUSA and Petersons, that provide essay review services and, depending on your circumstances, these may be worth the cost. American publishers have also cottoned on to the anxious parent markets, selling books with titles like 100 Successful Harvard/Yale/Stanford College Essays.
Harvard has published a helpful section on their website called Application Tips, which is obviously geared towards their own application process, but can't hurt as you look at applications for other unis.