How much cycling experience do you have? and what kind of bike are you going to be riding? The right way to corner is different for different bikes, but I'm not going to tell you to countersteer if you haven't been cycling for a while because you'll probably end up in the ER. You probably won't have to worry about it much anyway, since there is little cornering (if any) in most tris, and unless you're trying to be very competitive, it doesn't matter much.

At this stage of the game, just relax, lean, and turn. If it's a sharp enough turn and you're going through it fast enough, give the handlebar a little push with your outside arm. I don't think I've ever seen someone turn too sharply (hitting gravel doesn't count), but I have seen people wuss out halfway through a turn and swing way too wide and into the dirt even though they could have easily made the turn.

Cornering is very much a confidence thing. You need to follow someone else going through a turn to find out how fast you really can go through one before you're comfortable doing it on your own. It's also not something that you can just learn in a weekend, either. For the race, just work on going fast between turns, and relax on the corners. Smooth is fast.

http://www.coachcarl.com/training_articles/cornering.htm

That's an article I like on cornering. Its pretty long and its is really directed at riders just starting to do criterium bike races, but a lot of it is relevant and helpful...