Deciding what matters (in a picture, exposure wise)

The nicest and sometimes most appealing pictures are taken with great lighting. Every degree of brightness in the scene is reproduced in the picture, nothing is really too dark or too bright to fit. If you look at the histogram, it is a beautiful shape, a mountain pretty much centered with nothing blown out or in total shadow. For example, this picture of a train south of Moosonee shot in 2008.
Usually, if you point your camera at a scene it will do a pretty decent job of coming up with a decent shot. Most cameras have built in software for evaluating a scene and deciding on the settings to use to end up with a decent exposure.
Sometimes what is front of the camera makes it difficult to get a perfect exposure.
All cameras have limited dynamic ranges. This is the range from the brightest to the darkest lighting that can be contained in a picture. I suppose it is a bit like the contrast range statistic advertised with tv sets and monitors. The nasty thing is that human eyes tend to have a better dynamic range than cameras.
When you get a scene that exceeds the dynamic range of your camera you need to decide what matters. Are there relatively dark objects in the scene that you want to show up with detail and colour instead of as dark shadows? Is there something that is really bright and beautiful that you want to show up properly?
The classic example is taking a picture of the rising sun. On a clear day, when the sun is not dimmed by clouds or fog, there is no way you should even be aiming at the sun. So the most memorable sunrise and sunset pictures include lots of clouds or are taken when the sun is not directly visible.
A more reasonable circumstance is when you are taking a picture and the sun is shining towards the camera. If you have a subject facing you, that subject is going to be a shadow if you want things lit by the sun to turn out propertly.

Yesterday I went to take pictures of work on the road to Moose Factory. This is a winter only route across the Moose River (pickup trucks started driving across yesterday). I didn't have much time (there are not a lot of hours of daylight right now and I am supposed to be at work for almost all of them). When I went to take the pictures what I saw was a group of  men out working on the glaringly bright ice. If I took a normally exposed picture they would be nothing but black outlines so I had to adjust the exposure. I had to let more light into the camera so that the workers and their equipment would be reasonably well exposed. The result is that the ice and snow and the sky are much too bright. Later I took a shot of a dark blue truck dumping snow at the same spot. I exposed my picture so that the truck would show up properly and hoped for the best with the rest of the scene. It is not great, the sky is completely "blown out" but the truck looks ok. That was my choice.

Most cameras have the ability to adjust the exposure to brighten or darken the picture. Sometimes this is express in terms of "f-stops" or "stops". Basically, if you increase the lighting by one stop you are doubling how much light is getting into the camera. You can do this by changing the f-stop or by slowing down the camera or by changing the ISO rating. Most of the time this is an easy adjustment. If you want to be fancier you can take an exposure reading from one of the subjects and adjust your exposure for that subject. It is probably faster just to grab a few pictures at different exposure levels and pick the one you like.

There are things you can do to make the best of this situation. On the computer you have some scope to brighten up dark areas and reduce the brightness in overexposed areas. This works even better if you shoot RAW pictures where you have a wider dynamic range than you might with JPG's. Your camera likely has a wider dynamic range at lower ISO ratings.

If you have time you can take a bunch of pictures at different exposures and combine them on the computer. This is called High Dynamic Range (HDR). You have one exposure that picks up the details of the dark areas and others that handle the bright areas. Depending on how you combine them you may end up with a natural looking scene or with something out of science fiction.
Michael Freeman has a great book "Pefect Exposure" on this subject which divides all pictures into twelve different types of exposures. It is not overly technical and has a tremendous amount of information.