To follow up on my previous post on photographing sports and freezing action, an opposite but equallyinteresting technique is to use shutter speed to show motion.
To freeze something moving quickly requires a fast shutter speed.
To "unfreeze" it, and to show it's motion, requires a slow shutter speed.
Granted, a slow shutter speed 1/60, 1/30, 1/15, 1/8, 1/4th of a second a so on, will blur motion in your photograph.
Realize that if you slow your shutter speed down, handholding your camera can be difficult. Usually, most have difficulty handholding a camera any slower than 1/60th of a second and getting the subjects you want in focus. There will start being a blur simply from your hands shaking the camera slightly. You can get better at having a steady hand, but use that as a general guide. Anything really slow, use a tripod.
For example, if you want to photograph water running and want to get the water to that "whispy", "creamy" look....set your camera on a tripod and shoot the photo at a slow shutter speed.
This is where you need to experiment. Start at 1/30 and move your way slower to see the effects.
One of the reasons digital is great is the ability to immediately see the results of what you're playing with.
If you want to show motion in your photograph but to hand hold it, you can also try "panning".
This is where you follow the moving subject (and try to focus as you do this) but do so at a slow shutter speed.
The result is the subject in focus but the background blurring with motion from your panning motion.