There's a lot of things to look out for when buying a new snowboard. You need to find a board that will suit your style, so whether you're a fan of heading down the side of a mountain as fast as you possibly can or whether you're interested in gadding about in the park, there's a board to suit your style. If your feet are larger than average, you might be interested in getting a board with a larger than average width, like the Burton Custom Wide (or any number of others). You should be looking at getting a board that's got the right shape for your style, a board with the right smoothness, rigidity and a board that's concave exactly to your liking.
You need to find the snowboard that will mesh perfectly with your bindings (or failing that, find bindings that will suit your board). The board that will work with your stance, build, foot size, height and weight.
A good way of making sure you get the right snowboard for you is to get a few ideas of what you're looking for first - try to find some snowboard reviews and see what other people are saying about the boards you're interested in. Before you buy, you could always try renting the snowboard of your choice and spending a few hours at the snow dome or indoor snowboard park. See how natural it feels to you, see if it matches what other people have said and get a feel for how you and board work together. When you've found the perfect snowboard for you, you'll know it as soon as you try it out.
If it's your first board and you're not sure what to get and you've got friends that snowboard, you should think about bringing them with you to the snowboard shop, or getting them to find a decent bargain for you online. It can be particularly difficult if it's your first board, because it's so hard to know what's good and what isn't until you've tried it out. You could just choose the one with the coolest design, but you'll probably regret it if the board itself doesn't suit how you ride. If you're going to drop some serious wedge on a board, then you definitely need to check out the reviews online first to make sure that it's a decent board.
Good luck hunting for that perfect snowboard!
Dave is a keen snowboarder from the UK, and runs the snowboard blog/magazine/store Snowboard Central. He encourages snowboarders to leave reviews of their boards at Which Snowboard, a reviews site that he runs. He also likes drinking tea and is permanently plugged into his iPod.