Do you have the game window on one monitor, or both? I've never used multiple monitors for any game other than EVE, so I'm ignorant when it comes to this. But I finally got my CoD addicted brother to play WoW after a decade of failed persuasion, and he's having a blast except that he hates alt-tabbing in games so much that he has two monitors in order to avoid it. Having boosted his first character from 11 to 100, during a major pre-expansion, he's completely lost when I'm not on, which leads him to having to hit up wowhead regularly. He can't figure out how to accomplish having the game window just fill one screen so he can have his browser on the other.
Any help or guidance on how to accomplish this would put me in your debt. I'm afraid that he's going to quit if he can't get this resolved in some way.