Camera still, lens zoomed: Use a tripod again, plus a lens that you can zoom, say from 70mm out to 28mm. Shutter speeds of more than a second work best for this technique. For a 4-6 second zoom, I start with 70mm. I hold this for a second or 2, then quickly zoom to 50mm, hold, zoom to 35mm, hold, finally out to 28mm as the shutter closes. This also takes practice. Count down the time as you zoom. Soon it'll become very easy. Remember if you don't like it, or went too fast or too slowly, just delete and try again.
Try this with a stationary subject/scene first. Then try it with moving subjects. Naturally, slower moving subjects will give a more satisfactory blur.
Lens zoomed while camera rotates: This is a technique that I recently tried. I have some friends who do use this technique and have produced very intriguing images. If your zoom lens has a rotating collar, then hold the camera by the lens collar with one hand while rotating the camera body around the collar. You'd think this should be fairly easy to do hand held. It isn't! So this technique is best done with the camera mounted on a tripod. You need a ball head or other type of head, like the horizontal pistol grip head that is easy to rotate. I don't know how one would zoom/rotate with a lens that has a push/pull collar. Again, as with most of the above techniques, try this with stationary and moving subjects.