Photo: Streams of Motion - John Varley
The above photo is an absolutely perfect lesson in long-exposure photography. To get a shot like Varley's here you have to do a few things.
First, you should make sure your ISO (sensitivity of the film/sensor) is as low as possible. I mean LOW.
Second, you make sure that you have a relatively high f-stop or aperture. A smaller aperture opening means that more in the shot will be focused and you'll have what's known as a "deep depth-of field". Just remember that a smaller opening correlates to a bigger f-stop. Normally f/11 should suffice but you can definitely go even higher.
Lastly, but most importantly, you'll need to have a very, very, very, very, very, very, very, very slow shutter speed. In fact, the previous steps I've outlined here (especially the ISO) are really only meant to create the conditions for an extremely slow shutter speed.
Have at it! And happy shooting :)