The truth is, explaining the best ways to prep for each of the ACT's sections is beyond the scope of this article. There are literally entire books written on this subject. And there's your answer -- go get a few of those ACT prep books and use them. There are also ACT prep classes available; whether you want to take the classes or just use books is up to you and how confident you are in your ability to handle the types of questions the ACT is going to throw at you. At minimum, you should study a few of the prep books so you're familiar with the sections and the format of the questions. This will take a lot of stress away come test day, since you'll know exactly what you're in for.
A lot of ACT prep books have sample questions and even sample ACT tests included. Be aware that ACT does not license out old tests for publication. Some test prep books do a good job of writing sample tests that look very similar to actual ACT tests, but the only way to get an actual old ACT is to order one directly from ACT [source: Martz, et al.]. It's probably a good idea to do this, in addition to whatever other preparations you undertake.
The ACT is actually pretty easy to study for. It tests specific knowledge areas, so it doesn't include word puzzles or intentionally confusing questions. Once you know exactly what kinds of questions will be asked, you can identify the areas where you're weakest and study those. You can also focus your study time on areas with the most impact. Are you totally clueless about elementary trig? That's only four questions on the entire test, so save that for last. Brushing up on your algebra will be time better spent.
Finally, if you have a pretty solid idea of what you want to major in when you go to college, it's a good idea to focus on that subject area. When you tell a college admissions officer you want to go to their for their excellent physics program, a sub-par science score on your ACT will not look good. Of course, you might not have any idea what you want to major in until you've been in a college for a semester or two, in which case this strategy won't really help you.
For more information on preparing for college, take a look at the links on the next page.