The SAT is different every time it is given. Some are released after they are given (see links for "verify scores").
For the most part, the SAT is supposed to be an aptitude test rather than an achievement test. In other words, the SAT is designed, more or less, to measure intelligence. But of course, one has to be intelligent to get a super high ACT score.
For the reason cited above, SAT Math is different from school math. And most college-educated adults, no matter how much advanced math they have taken, are never able to do all of the math problems on the SAT. In fact, I've had many students who had A's in their calculus classes but who could not understand some of the SAT Math questions, even some of the percent and fraction questions.
The SAT Essay is unlike anything most students have ever done in school. And for many reasons, it has been criticized.
During the first lesson, I like to go over the PSAT if the student took the PSAT. The PSAT can be found online under Quickstart. If a student has a released SAT, I can go over that.
For almost all of my SAT/PSAT students, I use the 2nd edition of "The Official Study Guide to the SAT" (see above), which is by The College Board, the maker of the SAT and PSAT. The book is around $20 on Amazon. It has 10 practice tests, some of which are actual SAT tests. If a student is particularly motivated, I suggest studying vocabulary books and flashcards. See my "SAT Reading List" page.
Normally, I assign a practice test or part of a practice test for homework (but homework is optional, of course). Obviously, at the beginning the student should not time these sections. Worrying about time shouldn't become an issue until two weeks or so before the test. Clearly, the first step should be learning how to correctly answer the questions, not learning how to shave off seconds.
The student should star or otherwise mark each question that seems difficult. I prefer that students do not guess when doing homework, for obvious reasons (I hope the reasons are obvious!)
After the student is finished with the test, the student should grade it carefully. The answers are at the end of each test.
During tutoring, the student and I will go question by question through all of the questions that were missed or starred. I use a grammar book by Diana Hacker, along with other resources, for the writing and reading sections. Many SAT Math problems being designed to have multiple solutions, I love to show students different ways of doing the same SAT Math problem.
With some students, I throw in some non-SAT questions, but for the most part, I stick with The College Board book.