First, go to a local skate shopI'm not talking a mall chain store, like Zumiez. I'm talking a locally owned and operated skateboard shop. You should be able to find one in the phone book, or online (Yellowpages.com is a good place to start your search). Once you've found one, you can look around at what they sell, and ask the person behind the counter for advice. There are some big-name board brands that should be in most shops, but there are also lots and lots of smaller brands out there who you might like. Maybe there's a local skater making skateboards who you could support. Or, maybe that guy's boards are terrible! The people at the shop (both workers, and other skaters there) should be able to help you out.
Another bonus of shopping at an actual skate shop is that you get to see what the boards look like in person. Most skate shops will have a cool wall of boards, and it's fun to just stand there and look at all the graphics. If one jumps out and grabs you, then you can ask the shop owner about the brand, and if it's a good one. There's nothing wrong at all with buying a skateboard deck because you like the graphics!
But, what if you live somewhere that doesn't have a local skate shop?
Second, ask around!You can get a lot of the same advice from fellow skaters. Some of it might not be as informed or educated as shop owners - and some might be flat out bad advice - but it should all be sincere! Most skaters who I've met are actually pretty cool people, and they should be happy to tell you what they think about which skateboard deck you should buy.
If you don't have a local skate park, or are too uncomfortable to walk up to people and ask, you can also ask around on the Skateboarding Forum. People there will be happy to tell you what they think.
Third, check out reviewsFinally, the last suggestion I have is to check out the Skateboards Reviews. There are plenty of decks in there to read about, and to see which ones I've tried and liked. However, the list isn't exhaustive - there are PILES of skateboard decks that I have never ridden, and so don't feel comfortable telling you if they are good or not. Shoot, with all the small up-and-coming skateboard companies out there, there's no way I can know what kind of boards will even be available in your area!
Hopefully, this helps get you on the right track in picking out a skateboard deck. On a basic level, you really can't go too wrong. You might get a board that's not as strong as some other brand, or that turns out isn't quite as well made, but no skateboard lasts forever. By their nature, skate decks are built to be smashed. So, my most valuable piece of advice for you would be to not sweat it - ask around, get a board you like, and go ride it! If you don't like something about it, well, it'll be broken soon enough anyway! Have fun!