Mostly it's just a matter of signing up for one and
going.
This is likely to involve some travel, possibly booking a hotel, and so forth. Most big
GTs have their own forums and/or other official channels (blogs, forum posts) where the organizers answer questions and give guidance about the hotel, parking, answer rules questions, etc. You might check out the
NOVA thread for a great example.
It can be a really good idea to arrange the trip with a friend (or more than one) and gaming buddy. I usually travel with at least one or two friends and buddies so I have people to plan with, practice with, hang out with at the event and share war stories over food and beer between rounds and after. Of course, if you start attending regularly you'll make friends at the events, and see them regularly, and every event becomes an awesome "Hey, how you doing?! Let me show you my awesome new army/let me see your awesome new units!" meet and greet and old home week. It's really fun.
There's also a great general tournament preparation article on here. Let me dig up a link...
http://www.dakkadakka.com/wiki/en/Tournament_Preparation_Guide
There you go. The armies mentioned were popular in 5th, so that's not as applicable, but most of it's just really good general advice.
The key things to remember for your first couple events are that you should mostly be focused on learning, seeing a bunch of awesome new armies, meeting people, and having a good time. If you're super competitive you can try to win it, but if there are 50+ guys and only one Overall Winner, it's silly to make your satisfaction and enjoyment of the event dependent on being that one guy. Odds are high that you'll be among the other 49+, so you should make sure your focus and attitude allow you to have a good time even if you don't win.
If you have any specific questions, you can also post them here. Many of us regularly attend big events.