Just for clarification, the SAT is the Scholastic Aptitude Test. The ACT (American College Test) is an Academic Achievement Test. The difference between an Aptitude test and an Achievement test is important and is reflected in the way the test is constructed. An Aptitude test is supposed to measure your general ability to learn new information in the future and successfully adapt to the greater rigors of college coursework -- therefore they test general skills at a high level, such as vocabulary (a reflection of the amount you have read and your ability to retain information. The more you've read, and the more challenging works you've read, the greater your facility with words, and the better you'll do identifying synonyms, antonyms, analogies, and answering conceptual questions). Verbal comprehension has to do with your general ability to read difficult material and distill the important bits quickly.
The math sections again require a lot of basic knowledge applied in unique ways. Can you quickly figure out how to do logical math problems and do you understand complex math concepts? If so, you'll probably fare well when faced with college-level courses. The writing section has been introduced instead of the old critical thinking sections because too many students were beginning college with a total inability to write a coherent sentence.
The purpose of the SAT is to level the playing field between difficult schools, where a 4.0 is difficult to achieve but the students are very able, and easy schools where GPA is deceptive. The SAT is generally used as a cutting score rather than an absolute standard for admittance (they generally have a set of standards at a school and won't look at people who score below a certain point. School publications will generally tell you the average SAT of incoming freshmen, and you can guess that their cutoff is well below the average score).
As far as studying for the SAT, it won't really help due to the format of the exam. That includes expensive courses that promise significant point gains for taking the course. Research shows that it just doesn't happen. What CAN help, however, is taking practice tests from a book you can get cheaply at a bookstore, or ones you can download from the SAT website. The reason that can help is that the directions can sometimes be confusing if you open the book for the first time and are not familiar with the format. No sense wasting time reading directions. You will speed up a lot by practice. Note every question and type of question you get wrong in practice and look up how to solve those correctly. Look up every word you don't know. I can guarantee you'll do better and feel more confident when you know what to expect. It really is not too hard.
The ACT is specifically designed to test the factual knowledge you should have acquired by the time you are a high school senior. That's why there are area subtests -- like history, math, science, etc. The better the school you've attended, the more you should know. In theory, it should relate much better to GPA, and be less correlated with general Intelligence than the SAT. By looking at what you've already learned at a high level, it is supposed to better predict how you specifically perform in college courses. (Supposedly, the SAT is not related very highly to college GPA, so the ACT is supposed to make up for that).
The reason for the different areas of the country choosing different tests reflects a number of choices colleges make (it's a myth that only the east and west coast use the SAT -- it's used all over depending on the prestige of the school and the number of applicants). Elite schools tend to use the SAT because they want the best and the brightest even if they haven't always achieved well in high school (ever know anyone really smart but bored with high school? That's what they're trying to capture -- the undiscovered genius). But they'll also pick students with lower SAT's if they'll add something to the school mix -- like being a good athlete, an artist or actor, or a good gymnast.
You can study more to improve on the ACT than the SAT since it is supposed to be content-specific. But the dirty secret is that the correlation between the SAT and the ACT and general intelligence tests are remarkably high. You take the one that gives you the best chance of getting into the school you want, and you take both if you're applying to a variety of schools. Most of all, remember that a good breakfast and a good night's sleep will be more beneficial than hours of cramming and worrying.
Lastly, the quality difference in the education you receive between Harvard and State U. is not as great as you would believe. The difference is in the prestige and in the mean ability level of the student body. There is more variation at a State school, but you can also rise to the top more easily. Small private schools are also wonderful and often have more generous admission policies. And it is often easier to get into a smaller school, do well, and transfer to a more prestigious school as a junior than it would have been to get into the better school to begin with. One test will never decide your fate.
So relax, do what you can, and pray about the rest.
(if you want more info, you can go to their websites: