A lot of people (including myself until just recently) do not realize how photographers, like in National Geographic, are able to get those waterfalls, streams, etc. to look so smooth and beautiful. Well we are all in luck because it depends simply on an adjustment of shutter speed for your camera.
DSLR cameras have a function for shutter speed (Tv) that allows you to slow down the opening and closing of the shutter from portions of a second to minutes. Most photographers regularly shoot at 1/125 of a second; however, to get the smooth water effect you need two things: A longer shutter speed and a tripod.
The shutter speed can be anywhere from 0.5 seconds to 10s (or whatever you choose that works best for your scene.) Play around with the Tv time settings to see what will work best for you photo because too much light can overexposure and cause your image to be too white.
YOU NEED A TRIPOD (or a place to sit your camera.) No matter how steady your hands are it is best to always use a tripod because 1 second might not seem that long now, but you are risking having camera shake mess up your breathtaking photo. You can pick up a tripod for fairly cheap at most major retailers that offer electronics.
For example, the photographer (not me) who shot this stunning photo has a shutter speed of 1/3 second. That still seems pretty fast, but not in camera terms. This shutter speed can be painfully slow for some photographers, but look at how wonderful the photo turned out.
An edit will be made to this post to show you guys some photos from my own collection for a clear difference between shooting a waterfall with a fast shutter speed and a slow shutter speed.