The Great Barrier Reef, if you were to do a Family Feud-style survey of "things you think about when you hear Australia" this would probably be right up there with kangaroos, koalas, and Vegemite. Made up of over 3,000 individual reef systems, it's also the only living thing you can see from outer space!
There are plenty of towns and islands that you can visit to see all this natural beauty. To plan your visit better you can visit their official website. For my trip, I stayed in Cairns, a laid back town with plenty of tour and boat options. I spent my day with Silverswift, a company that has great options for snorkeling and scuba. They were very professional and helpful with everything.
My suggestion is to go to a tour agency (there are a ton in Cairns) or ask your accommodation for suggestions. Be honest with your diving/snorkel experience and expectations for your trip, as well as budget. They can offer you the best option. Even if you can't swim don't worry, I met a girl who went out. She said she was given a life vest and an instructor to hold onto. November to about May/June is stinger season, this means you'll have to wear a protective suit, it's not that much of a hassle though.
After you've got everything booked, you can show up and spend a fantastic day in the ocean! If you're in the documentary mood, ask about underwater camera rentals.