To avoid red eyes in your photographs, make sure that your camera either has built in red eye reduction or you change the direction of your flash. If you did shoot a photo and it contains red eyes, you can easily remove them through the use of a graphics software such as Corel or Photoshop.
Make sure you have a focal point for your photograph. This should be the first thing that the viewer's eye is drawn to. Whether it's a flower, a person, or a bird, every shot you take should have a specific focal point. Don't only think about what the focal point is, but figure out the best spot for it in the shot.