Hi! I'm currently in year 13 taking my A-levels, and I have a place at Vanderbilt University in Nashville, TN, with full financial aid, so I know a lot about the application process for US universities.
It depends what year you are in. If you are currently in Year 13, you would have to take a gap year and start your application in October (Deadlines for Early Decision [binding entry] are usually 1st and 15th November, depending on the uni, and 1st and 15th January for Early Decision 2 [binding entry, only some unis do ED2] and Regular Decision) for 2019/20 entry.
If you are in Year 12, you apply this October (same details as above) for 2019/20 entry.
If you are in Year 13 (and definitely want to study in the US and take a gap year) or Year 12, you should sign up for the ACT or the SAT right now.
If you are not in Year 12/13, you should take the ACT in Year 12 and you will apply at the start of Year 13 (October time).
You need to take either the SAT or the ACT. Your A-level grades cannot be converted into an SAT score. You still need to complete your A-levels and receive a final grade. Have a look at both the SAT and the ACT, and see which one you prefer. Please be aware that it can cost up to £100 to take these tests.
If you are applying for (a lot of) financial aid, you need to be a very good applicant. To be honest, even if you aren't applying for financial aid (keep in mind US unis are expensive and you and your family will be expected to contribute), you still need to be a good applicant. For Harvard Class of 2022, the acceptance rate was 4.6%!
A good applicant consists of: stellar extracurriculars and honours, great A-level predictions and GCSE grades, good test scores (although not always the case - I have a 30 and Vanderbilt's 50% range is 33-35!) good essays, and good letters of recommendation.
It is a lot of work, but definitely worth it in the end! I've gave a broad overview of the things required, feel free to ask any questions!