Admissions to US schools (to me) are simpler and much more clear-cut than university admissions in the UK.
Your DS should take the SAT the year prior to applying to schools. It is not a difficult exam - a maths section, and english section (vocal and comprehension), and a short writing section. A couple of months with a good practice book and some timed tests should suffice.
The summer prior to the year of applying, you call around to the Universities to receive applications. They usually consist of 1-2 personal statements, plus some shorter written parts, a copy of your son's school transcript (sent directly by the school), 2 external recommendations (can be teachers, head, mentor and also send directly by the referee), a copy of SAT results and any achievement tests taken (these are subject tests - just a couple chosen ones are taken, are they are not immensely important - just show how your DS does in a subject compared to the national average).
One key area whose importance is greater in US Uni applications are your sons extracurricular activities - these should be done to a high level, and really differentiate him. High level sports, political involvement, meaningful volunteer work are all helpful. I personally know someone who was a B/C student with mediocre SAT scores who was admitted into Harvard because he had written and published 2 comic books whilst in High School.
Due dates for admission are usually in October (for Early Admission/Early Decision) to November. Mid April is the time most decisions are mailed out.
There are many more excellent universities in the US than in the UK, and they are not just Ivy League. There is a whole tier of Universities with no graduate departments (so only focus in on the undergraduate) which are called Liberal Arts Colleges which are superb (Amherst, Williams, Swarthmore, Haverford, etc). Some top non-IVY universities are MIT, Cal Tech, University of Chicago, Stanford, Duke, Wash U (Missouri). There are also top State Universities which are as good as the privates, but have a different feel (great College football teams for a start!) such as University of Michigan and the California schools. As you can see, loads of choice (I have omitted at least 30 other big names)and diversity.
Additionally, the very well endowed schools (and there are a large number of them) offer extremely generous financial aid packages (eg, for parents with a combined income of less than £75,000, Harvard will provide tuition, stipend, and air fare).
Good Luck!