Our friend Lassirra (who has just recently started writing Scattered Shots for us here at WoW Insider) has a great post over on her personal blog telling Hunters how to apply for a guild, but really, most of her advice would work for anyone trying to move on up to a better guild situation. I've long said that one of the key indicators of a guild worth getting into is that they require you to apply, so following these tips when actually filling out that application will very much help you find your spot in the game, whether it's raiding at the highest levels, teaming up with other PvP afficionados, or just getting yourself in the right casual circles.
The first few suggestions are just about following the rules: answer all of the questions, don't be weird, and don't put anything on the app (like major drama in your history or major spelling errors or offensive language) that would let the guild's officers give you a definite "no" right away. Second, know your character and your class. As Lassirra's twitter people say, the standards for most guilds' recruitment (even great guilds) are pretty low. As long as you're easy-going and you know how to play your class and have an interest in bettering your character, you're going to be pretty much instantly accepted into 90% of guilds out there. You don't have to throw together a big Flash presentation (though it might help).
And finally, don't worry about rejection. This may all sound like applying for a job, but it's not nearly that serious -- if one guild decides to pass on your app, go find another one you like and apply there. The extra time will be worth it: if all you've done in terms of being in a guild so far is join up with someone shouting in the Trade chat, you owe it to yourself to, as Lassirra says, put the time in to find a guild that's right for you.