In most portrait photos, the subject's eyes look directly into the camera. Have your subject express a variety of emotions to capture a unique photograph. You could also try to have the people in the picture look at something in the frame.
A great photography tip is to make sure your shots have depth in them. An easy way to achieve that is to be sure that you have a background, a middle ground, and a foreground. Having all three of these will give your pictures a sense of atmospheric perspective.
Don't be afraid to experiment! With digital cameras, you can now store an incredible amount of photos. Try it out! Don't be afraid to set up your camera at a stream one day and play around with the effects to see what kind of photos you get. It can be a great way to learn what works, and what doesn't.