(This is a work in progress, started 9/3/08.)
Photography is all about the light. In order to take the photos you want with your DSLR camera, you need to understand the nature of how your camera captures an exposure.
In its simplest terms, your camera is just a box that allows light in to capture the scene before you. Too much light, and you'll get an overexposed picture, too little and it will be underexposed and too dark. There are 3 ways that we can control this light - Shutter Speed, Aperture, and ISO.
LIGHT BASICS
Your camera will pick up any light - whether it be the sun, camera/studio flash, or lighting. The amount of light entering the camera depends on the time your camera allows light in - the shutter speed. A slow shutter speed will let in more light than a fast shutter speed, providing more light for your camera to work with.
This light coming in is controlled by an opening that can either be very small to let little light in, or very large to let alot of light in. This is called the aperture, or f-stop. A wide open aperture is equal to a small f-stop and lets the most light in.
The shutter speed and aperture work together to create the exposure you want. Depending on the lighting, and the effect you want, the aperture opening works inversely with shutter speed to bring in the optimal light. If your aperture is wide open, light will pour in, so you'll need to make sure the shutter speed is fast enough so you don't get too much light and an overexposure.
You'll find that there are several correct exposures you can achieve by adjusting your shutter speed and aperture. This is discussed below in the "Creative Effects" section.
Finally, ISO completes the exposure triangle. ISO controls the sensitivity to light. So if you're shooting indoors or in shade, you'll want to increase this sensitivity so your camera will be able to work with more light. Watch out though, too high ISO will introduce noise! So you want your ISO to be as low as possible for the situation. Outside in the sun, you'll set it as low as it can go, perhaps 100 or 200 depending on your camera. In shade, you may need to increase ISO, and the darker the environment, the higher you'll need to go to capture a correct exposure.
CREATIVE EFFECTS
Once you understand the relationship of shutter speed and aperture, you can test out some creatively correct exposures. Focus on shutter speed to achieve either a blur or freeze-motion effect. Focus on aperture for depth of field control. Depth of field is the amount of the picture in focus.