If you are having difficulty holding your camera straight, purchase a tripod. A tripod will go a long way in helping to keep your camera in place, so you can focus on other variables other than balance. Tripods work great if you are in the wilderness or on an uneven terrain.
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.
Play with the shutter speed on your camera to catch unique and wonderful photos. If you have the right shutter speed, you can get beautiful photos that would normally happen so fast that the human eye couldn't process it fully. Try experimenting with shutter speed and a tripod at a stream or waterfall for some great photos.