Keith, re the waterfall, it may actually be impossible. The problem is that your camera's sensor simply can't cope with the huge difference between the light and the dark areas; it doesnt have enough dynamic range (no camera will be much better; none are anywhere near as good as your eyes).
The water looks pretty well exposed to me, so even the slightest increase in exposure, to make the dark bits lighter, WILL overexpose the water (make it brighter), at least a bit.
In auto, there are only three options I can see if you want a more balanced exposure:
1) take bracketed shots, meaning taking three or more shots, with one at the camera's chosen exposure, one or more below, and one or more above (your camera will have a setting to do this automatically), then choose the one that gives the best compromise.
2) do the same, but merge them together afterwards using software, to create a high dynamic range (HDR), photo.
3) adjust the exposure in just the dark areas in software afterwards. This works much much better if you've shot in raw format, and even then isn't a magic solution; you can only go so far without getting a lot of noise and other problems.
There are other things that can be done if your subject has a very wide dynamic range, such as using graduated filters, a black card technique, or exposing for specific parts of the scene, but some wouldn't work for your scene, and some require more practice and understanding of exposure than you can be expected to have as a beginner.
Regardless of all the above, I'd strongly suggest coming out of auto. All the time you use auto, the camera is making all of the decisions for you, so really you're not learning much because there are too many variables that you're not controlling and you're trying to second guess the decisions your camera's software is making. You need to start experimenting with the settings so you learn what effect they have.
You need to understand what affects exposure, how your camera deals with it, and how you can control it. These two tutorials are pretty good starting points.
http://www.talkphotography.co.uk/forums/showthread.php?t=158332
http://www.talkphotography.co.uk/forums/showthread.php?t=79229