In this video from Broncolor featuring Karl Taylor and Urs Recher, we learn how to combine two different kinds of lights in dance photography to capture motion blur and frozen detail. While they are using high-end Broncolor HMI lights with Broncolor Siros flashes, these concepts of working with flash and ambient light can work on any budget.
The key, of course, is setting your camera to rear curtain sync, so that the flash fires at the very end of the exposure, which gives you the detailed subject with the motion blur trailing.