Wear a life vest. It doesn't matter how hot it gets outside or how uncomfortable you might feel in that vest.
If you're going on a class 1 or class 2 river, you don't need a helmet. But if you're headed to a class 3 or above, that helmet, like the life vest, can save your life.
When you're rafting with others, keep your paddle down and near the water. When you get excited going through the rapids, this can be very difficult, but it will help everyone else in the boat.
Don't go out alone. You really shouldn't even go out with just one raft. To be really safe, you need to have more than one person in more than one raft.
When you're going out on a whitewater trip, make sure that you make a plan of where you will go and when you will be back. Then, be sure to tell someone else that's not going where you will be and when you plan on returning.
Before you go, check out your raft, paddles, and any other equipment you're taking on the trip. A few minutes of checking the air levels of the raft and the paddles for cracks can save you a lot of trouble and a lot of time once you've started down the river.