The nice thing about using manual on a digital camera is instant feedback via the LCD screen. As Luke said, you really need a good grasp of ISO, aperture, shutter speed and depth of field. These concepts were probably a little easier to grasp on an old film camera because of how the f-stops and shutter speeds were arranged.
Here goes the jist of it (using film camera f-stop and shutter speeds).
Most (film) cameras can have the shutter speed changed in increments such as 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000. If you look at these numbers you will notice that each one is half as long as the previous time. Basically, if you use a shutter speed of 1/125, you can increase shutter speed to 1/250 and let in half as much light or you could slow it down a to 1/60 and let in twice as much light. That should be fairly easy to see...open the shutter half as long, you get half the light, open the shutter twice as long, and you get twice the light.
How does the aperture play in to all of this? Let's say that you have you f-stop set on 5.6 and a shutter speed of 1/125. If you decide that you need more light you have several options. One option would be to change your shutter speed to a longer value to allow in more light. The other option would be to change my f-stop or aperture. If I go up one f-stop to an 8 I will let in half the light (just like increasing shutter speed) or I can decrease the f-stop down a stop to 4. This will open the aperture twice as much allowing in twice as much light (just like decreasing shutter speed).
So, evertime the shutter speed changes, it lets in twice the light, or half the light.
Each time f-stop increments, it lets in twice the light, or half the light.
Just from that you will see that there are a number of settings that will generate the same exposure... an f-stop of 5.6 and a shutter speed of 1/125 will yield the same exposure as an f-stop 8 (lets in half the light) and a shutter speed of 1/60 (lets in twice the light). Or you could open the f-stop to 4(let in twice the light) and a shutter speed of 1/500 (let in half the light).
So what is the difference between these settings? Depth of field. The smaller the aperture (larger the f-stop) the greater the depth of field (more stuff in focus). Larger aperture (smaller f-stop) gives a shallow depth of field. So which f-stop you choose will be dictated by the depth of field that you desire. That will then dictate you shutter speed.
ISO or film speed works the same. If you have your camera set on ISO 100, f-stop 5.6, shutter speed of 1/125. If you need to let in twice the to get a correct exposure, you can open the f-stop 4 and let in twice the light, or you could change the shutter speed to 1/60 to let in twice the light, or you could change your ISO to 200 because it only requires half the light that ISO 100 needs. ISO 400 only needs half the liht of ISO 200. Do you see the pattern here?
With so many settings all yielding the same reults (exposure wise) you can see why it is good to be able to shoot in manual mode. Everyone of these settings will play a part in how the final image will look. Why use auto settings and let the camera decide, it has no idea what you are trying to capture...only you do.