Zodo from LFG KZ recently sent us a link to a post on his blog about "guildshopping on a new server" (yes, I know it's spelled wrong on his site, give the guy a break). If you've recently transferred servers or have just rolled up a new character and are looking for a good guild, it's definitely worth a look.
There are a few things I disagree with in there-- I find it really hard to believe that small servers don't have high level raiding guilds, and in my experience, a bigger population may theoretically mean lower prices, but in practice that's not always true. But his later steps are good ones, especially making sure you put in the research on where a guild's at in terms of progression (some guilds will help you get to their level, but most really high level guilds would rather you're already up there with them), and what classes they're interested in recruiting. Even if a guild says they're not recruiting, being nice and chatting with someone from the guild (in a city, as Zodo says, not in a raid), can clue you in on at least how you might get a trial run with them.
And applying for guilds is something very basic that everyone trying to get into a great guild should be more than happy to do. I used to be in the camp of "lol it's just a game i'm not applying," but the fact is that the guilds that seriously ask for (and consider) applications tend to be the better guilds to be in, and so the few minutes spent filling out a form intelligently is more than worth it in the long run. If you're about to face this situation, Zodo's guide is definitely worth a read.