Picking an Object:
When you shot close to the beginning or end of the day you may be looking for the contrast that great, horizontal light gives you. But if you you're shooting sunrise or sunset you're almost certainly looking for the color, and probably the color on the clouds. None the less, even with wonderful colors, you need a focus for your photo. I've shot quite a few images with great colors and no interest whatsoever. You need something to focus on.
The sunrise with stars, but no good subjects
A similar image, some mountains in the background and good colors, but no strong objects to bring focus to the image
The above images show the danger of the sunrise (and believe me, they are dangerous!) To the eye, the colors are spectacular, but without a strong object in frame, the image ends up without appeal. It can be hard to find good subjects, the exposure you need (see below) causes just about everything other than the sky to become a silhouette.
Yet you can use the low-light to your advantage. The clouds can become subjects, and any reflective surface on the ground suddenly becomes clearly defined and just as colorful as the clouds.
Clouds and a lake
It's not a great image, but it shows how the low-light highlights certain elements. Here, it's a lake but sometimes just a cloud can do it.
The object is a cloud, wow, right?
Here the focus is on a cloud: something that's a lot harder to pull off without a sunrise (or set), but the key is that there's an object in the image: not just colors.
Fire at dusk
One of the great things about sunrise and sunset is that it reduces the image to swaths of colors and shapes: about as close as you can get to a painting. Often photos are too busy, simply because you can't take things out of nature when taking pictures and often you're image is overloaded with extraneous details. The low light and wonderful colors allow for a much simpler approach to the image and your ability to get creative takes off.
Choosing an Exposure:
The most important thing for most sunrise/set photos is to get good saturation and that's not going to happen if the camera remains on its default exposure. Unless the whole frame is taken up by the sky, the camera will try to balance the sky and the ground and end up over-exposing the sky and thus not getting good saturation where all the colors are. As was mentioned above, properly exposing the sky will most likely obscure anything but the shape of the landscape, but that's just the way it is. The light balance changes quickly as the sun comes up or goes down though, so you get different shots from minute to minute.
Mix of exposures in the image to allow for the colors to come through
Here you can see a pretty dark foreground so that the pink hue shows up on the horizon. The objects still show up, but are almost entirely defined by their shape. It makes for a much different image then when fully exposed. The textures and colors are gone from the foreground but the structure remains.
Fire and Ice
For this photo, I decided the foreground was more important then the colors of the sunset. So the sky (and colors therein) are blown out but the snow in the foreground remains distinguishable. Here the sunset serves to provide color to the ground rather than the sky or clouds. A brighter exposure is used in this one.
Clouds hover over Longs Peak
Clouds are a must for almost any sunrise
Sometimes you get lucky, typically with mountains where the light on the ground is the same as the light on the sky. Then each can be properly exposed, though generally a lower exposure still provides better colors.
As a point of reference, I typically shoot about 2/3 of a stop below standard exposure. However, I often end up taking several versions at different exposures as each image requires something different, and the light changes so quickly.
If it's digital, and you haven't changed it, your camera is almost certainly set to 'auto' white balance. This works different ways in different cameras, but in general it bases the color adjustments on the idea that your image is color balanced. That it's basically grey when all summed together, and some each of red green and blue. It works pretty well for most photos taken in the outdoors, but not for sunsets that are dominated by red. I typically set the white balance to either daylight or cloudy. The latter adds red which can be good in some cases, but may end up making the image look fake. If you really want to boost the red you can select the 'shade' option if your camera has one. However, I would strongly recommend avoiding the auto setting.
One Final Note:
When setting exposure, I normally use the aperture priority setting. Because the light is so low I'm often tempted to use a very low aperture and thus speed up the shutter. This can work well in some cases, especially since almost everything you're looking for is out on the horizon (and thus pretty close to infinity and able to capture with a low DoF). What sometimes happens is when I shot with this low depth of field, even if the foreground is only silhouette, that silhouette is out of focus, loses defnition, and detracts from the image.
A clear silhouette of a mountain and a tree
Another image that required a significant depth of field
Other than that, sunrise and sunsets are like any other image: get a few technical details down, experiment, and in the end your image will be as good as your eye. Try showing up 45 minutes prior to sunrise, and staying 45 after sunset and you'll capture all sorts of wonderful colors.