Expressing the idea of motion in a still photograph seems like an oxymoron, but it can be done with a slow shutter speed. In addition to that, you can add a zoom where you change from one focal length to another during the slow shutter speed and while the subject is moving.
That's what I did with a Whirling Dervish in Turkey last year. The room where the performance was taking place had some construction materials in the background, and this was a way to eliminate the unattractive environment.
Note: Jim Zuckerman teaches many online photography workshops at BetterPhoto's digital photography school, including: Developing Your Creative Artistic Vision and Taking the Mystery Out of Flash Photography