The standardized tests are definitely out of place in the entire admissions process. The wikipedia articles on each test highlight the criticism displayed toward it, be it ACT, SAT, SAT II's, or AP's. The SAT acronym no longer stands for anything because previous meanings did not hold true. The test was not a good measure of Scholastic Aptitude nor was it a great Scholastic Assessment. Honestly, it doesn't test reasoning either. Regardless, I'll cover all the material in a little bit, but this bears mentioning first.
These tests are extremely important to colleges for one reason. They standardize the applicant pool on one numerical scale. This is unfortunate because the tests, which are supposed to predict freshman grades in college, do not perform up to par on this basis. High school grades extrapolate this factor much better. However, given different grade scales, grade inflation, and difference in curriculum in secondary schools nationally (and internationally), it's absolutely necessary for the colleges to have tests that allow them to compare students directly, even if on a completely arbitrary scale. These tests are very important at state schools especially, which do not have the time to read all the rec letters, all the essays, and analyze all the different curriculum and environment of each applicant. So, despite their clear disadvantages, colleges must use them.
Now, a quick overview of each test
The SAT
math: tests up through geometry with a tad of algebra II
critical reading: tests if you can read and comprehend passages and tests vocabulary (with a limited range of words)
writing: tests basic grammar knowledge and essay writing (through grammatical correctness, extent of vocabulary, and length)
The ACT
unfortunately I'm less familiar with the ACT, but to the extent of my knowledge, the math is slightly more advanced, the reading section is similar to critical reading in the SAT, the english section is similar to the grammatical section of the writing portion of the SAT, the essay is very similar, and the science portion tests very little true science and much more reading comprehension ad basic data analysis.
SAT subject tests and AP
These are the tests that actually test advanced material. The structures vary greatly between both AP's and subject tests, and greatly within the type of test as well. Generally though, the AP focuses on both multiple-choice and free response, and the SAT IIs (subject tests) focuses heavily or only on the multiple choice. Subject tests are also much shorter.
SAT vs. ACT
The ACT is more subject based than the SAT and much more straightforward when asking questions. However, it allows less time to complete question in the time allotted. The SAT is less subject based, llows greater time, but (the big one!!!) the writers of the SAT will deliberately give you duplicitous questions and attempt to deceive you. Taking the SAT isn't about having taken Calculus, Microbiology, and Essential Homer in high school. It's about making sure you are aware that the ETS writers will kill your score by giving you tricky questions, not that relate to difficult material, but that they phrase so will but down B instead of D every time because you didn't read carefully enough.
Breaking it Down
Now, I've never tried the ACT myself because I've performed sufficiently well on the SAT, but if you are starting early in the whole testing process (freshman year or early sophomore year), I strongly recommend you take at least a few diagnostic tests of each and compare scores. Then focus on the test you performed best on. Because the tests are formatted differently and test different abilities/material, you probably will consistently score better on one than another. And, because almost all, if not actually all, colleges allow submission of either test there is no heinous penalty of taking one over the other.
Once you have selected the ACT or SAT, study it and practice. Of course, time will constrain your ability to do so, but it's essential that you make time for the test. A friend of mine, now attending UC Berkeley, raised his SAT score from 1600 (of 2400) to 2200 between two tests simply by studying the test. He went from about 50th percentile to 99th. Just by studying the test.
Ok, so how to study you say? First, know your test. You should have learned plenty about it just in the diagnostic sessions already, perhaps even checked it out a bit before that. But I urge you, take a class or buy a book. Both can give keen insight into the structure of the test and how to take each section, how to handle each question, tips for saving time, tips for prioritizing. They will boost your score. However, obviously there are drawbacks to both methods. Classes will keep you on top of work with a timely schedule and will force you to se techniques, do homework, practice, etc. But, books cost $20 as opposed to $1000 or more, and as long as you are diligent they will be just as effective. Some testing services also offer online programs, but I am not quite versed in the specifics.
Second, practice makes perfect. Many students boost their scores just by taking practice tests over and over. I suggest that you attempt to do a few sections a week. If possible, do 1 or 2 a night. Course, that's hard to accomplish, especially balanced against the rest of your life, but that much work will definitely make a huge difference. Also, try to take a full practice tests under testing conditions or take diagnostics with a testing company. Take a few of these a year, once a month if you can.
Otherwise, stay up to date with actual material on the test. Make sure you have all the math on your test covered. Pay attention to grammar section in high school english. Study vocabulary [I highly recommend you do this because most essays also test the breadth of your vocab, not just the vocab questions themselves. Also, many review books provide comprehensive lists of the vocab that is most likely to show up on any given test, making it easy to learn all the ones that are essential]. Above all, read plentifully. This will help comprehension on all sections of the test, aid vocabulary, make you a better reader, etc. etc. etc.
Finally, start early. If you start practicing in 8th grade or freshman year, you have a 3 or 4 year edge on everybody else. That'll make you a 36 or a 2400.
If you have any question regarding standardized tests, my contact should be below, and there are countless books about, forums over, and websites covering these tests. Do your research.