Many people like to see the milky look of flowing water. It helps represent motion. In order to capture the motion of water, you need to play with your shutter speed. Specifically you need to slow it down, usually in the range of 1 to 2 seconds.
Camera shake becomes very important to avoid when dealing with slow shutter speeds therefore you should use a tripod.
I would recommend beginners use the Tv mode on your DSLR camera (Time Value). Some cameras use an “S” instead of “Tv” for Shutter Priority. This will help ensure your photos are not overexposed by letting the camera automatically balance the other portions of the magic triangle (see my post on photographing the moon).
When adjusting the values in Tv mode, you will see values such as 1/60, 1/200, 1/1000, 1″ or 2″. The double quotes represents seconds. When trying to create the impression of motion with water, you may end up in the 1 to 2 second range (1″ – 2″).
Here is a quick sample photo I took. You can see there was a breeze that day. As I had the shutter open long, it captured movement on the leaves which makes them appear blurry. This was a glacial fed creek with heavy water flow. I ended up capturing this at only a quarter second (1/4) otherwise it was too white and blurry. You can avoid having it too over exposed (bright) by using an ND filter which allows you to use slower shutter speeds.
I recommend taking many photos when you have setup your camera on your tripod and experiment with adjusting different shutter speeds. When you review your photos later, one of them will stand out as your favorite. DSLR is great as you never have to worry about wasting film.