Dragging the Shutter: Long Exposures

One of the best ways to add visual impact to a shot is to combine still action with motion.

Clearly, in an example like the one you see here, there are certain 'rules' that must be adhered to. This includes selecting your subject carefully so it remains stationary while everything around it moves. You could do this with a single person standing in a crowd of moving people, or you can do it with a leaf surrounded by moving water. The trick to getting this right is to close the aperture to its smallest opening (this is usually f22 in a DSLR) and work in Aperture Priority mode. This effectively forces the shutter to open for a longer time to compensate for the small aperture, which in turn gives you blurred motion. To emphasize this always set the ISO to the lowest number. This slows the shutter speed further.
If you find that the motion effect isn't blurry enough, add a Polarising filter over the lens. This reduces the exposure by a further two f-stops, making the shutter drag for a longer time.
 

Canon EOS 5D MkII, f22 @ 0.3s, tripod.

If you like this effect, consider buying a neutral density (ND) filter. This effectively does the same as the Polarising filter but it's cheaper and can be bought in various 'strengths', ranging from one, two, three, and four f-stops of density. Buy a flat resin filter - these can be held over the lens to slow the shutter so there's no need to buy a set of them for different-sized lenses. A disadvantage is that because of the material they are made from, only one can be used at a time. If you combine two ND filters over the lens, it changes the color values. 
Oh! And use a tripod and self-timer.