Howdy!
I'd say the first thing you should figure out what LARP is right for you, both in terms of genre and play style. The Alliance LARP (us), for instance, is a medieval(ish) fantasy LARP that uses padded weapons and small bean bags to deliver weapon blows and magical effects, and running around in the woods, often in the dark. Our events are typically Friday night through Sunday afternoon, and players are more or less expected to remain in-character for the entire time, even when sleeping. If none of that sounds appealing (maybe you prefer sci-fi, or don't cotton to actually striking people with padded weapons), this one likely isn't for you (though there are other LARPs that might suit you better). If, on the other hand, that sort of thing sounds right up your alley, then your imagination has definitely found a home.
The first thing I think anyone looking to play should do is buy a rulebook. You can get it as a downloadable electronic version
here for under seven bucks, and peruse through it. You can also purchase a hardcopy through
our site. The rulebook has a good introduction to what a game might be like, tips on costuming and designing your character, as well as the nuts and bolts of how to play. Mike V (the owner of the whole shebang) has even posted up some sample pages in
this post.
Once you've given that a looksy, you should hit up the Chicago chapter's
out-of-game board and introduce yourself. Paul (the chapter owner) and his crew can give you details more specific to your area, both out-of-game (where they play, directions, their event/game day/practice schedules) and in-game (what is the name of the land that they play in, who's who, what kind of baddies to be on the look out for, etc.).
After all that, feel free to ask questions here, in Chicago's boards, or where ever else it might be suitable! Welcome aboard!
-JP