You need to be a strong swimmer because you might have to swim underwater, or in moving water. Always go paddling with another person—not just for times of trouble, but because someone should help you carry, load, and launch your boat, right?
Make sure your life jacket fits. Since paddling is an activity that you can do all through the year, leave enough room to put clothes under it when it is cold out. Be prepared to get wet! Take along extra dry clothing, just in case. Remember to keep sun proof with sunscreen.
Save paddling for good weather days. Since you don't know what mother nature will throw at you, know where your float trip will take you, spots where you can get out or camp for the night, and different ways to go in case unexpected trouble strikes your route. Avoid whitewater rapids, dams, and falls—only experienced whitewater paddlers should take these on.
Sure, you want all your friends and their stuff to come along, but don't put too much weight in the boat—you should have more than six inches of side between the top of the fully loaded boat and the water. Spread out the weight (including people) so the boat will stay balanced.
Take lessons to help you learn ways to get yourself back in your boat if it tips over—before you take your first trip. And then practice them. The main thing to remember is... Don't panic. If you can't get back in, stay with your boat and flip it back over—it'll float—and try to swim the boat to shore. (Remember, you're wearing a life jacket, right?!)