This Times article is spot on wrt the American university application process. It also details tests that must be done and outlines the financial aid situation.
All the necessary tests include maths at a high level, so if a UK student is not taking maths for A levels, he or she would need to somehow do a course up to pre cal level at least. In general, west coast universities require the SAT, while the ACT is more an eastern thing. Some universities require both. You would need to check with each individual university before signing up for the testing.
There's a fee for each application, ranging from $50 to $100 iirc. There's also a fee for each test, and each retake, and additional fees for sending the test results to each university you're applying to (under $20 each for this particular one).
The curriculum is extremely broad at undergrad level in the US, from what I'm familiar with anyhow -- again, maths is required for all in freshman year at minimum, plus a science, language, humanities subject, English. Some universities have core curricula that are very broad, even for those pursuing an engineering degree. Generally, you don't have to declare a major until perhaps your third (junior) year. As Mummytime says, there are vast differences among US universities. Thorough research is vital.
You don't get to specialise in something like forensic science until grad level, or maybe your final year, depending on the university. The best route to a career in forensic science is a bachelors degree in chemistry or biology (or major in chem and minor in bio) followed by postgrad specialisation.