A blog post by game designer Raph Koster (of Ultima Online and now Metaplace fame) will tell you how! Admittedly, Koster doesn't really go into much detail. Also, he's trying to help developers avoid hacking problems, not giving inside secret tips to hackers. It's still an interesting read, though!
He lays out an overview of the various design choices developers make that are exploited by hackers. For example, some developers might choose to trust the client to handle collision detection to reduce lag and increase gameplay responsiveness. Well, a clever hacker can make the client report to the server with false collision information, allowing that hacker to move through walls. It turns out that most designers take a middle-of-the-road approach, meaning that, as Koster puts it: "only bad-ass hackers are cheating, instead of damn near everyone."