Notification Center is a sweet new feature in iOS 5. Just swipe down the from clock and you can access it from anywhere. But in the beginning it will probably be overwhelming. That's because we've had all our notifications preferences set up around the old system - when we got a message, we could just read it, and then hit close and never see it again.
In the new system, they start to pile up in the Notification Center if you don't maintain it. Clearly, we don't want to have to "maintain" anything. That's why we got an iPhone, not an Android. Go now and spend 10 minutes and set up your notifications in Setting > Notifications.
Over the next couple days, when you get an notification you don't want or care about, just hop back in there and change your settings. It's always best to learn by just getting your hands dirty, but if you need help getting started here is a guide.