The simplest of all techniques is using a slow shutter speed to artistically blur moving subjects. When you do this, one of the best ways to create successful images is to show the moving subject sharper than the blurred background.
This technique is done with panning the camera such that you follow the movement. For photography panning, use a shutter speed in the 1/15 to 1/6 of a second range. This photo of an African white pelican was taken at 1/15th.