Zoom bursts can add an abstract quality to a variety of subjects including statues, windows and flowers. It can also give sports and action shots a dynamic edge. You can achieve a similar effect in Photoshop but there is more satisfaction getting right in-camera.
To create the blurred streaks and lines that emanate from the centre of zoom burst images you need a lens that will zoom. Trying different zoom lenses and changing the starting point of the zoom and the range you zoom through will give you different effects.
You're also going to be using slow shutter speeds so a tripod is an essential bit of kit and means you'll have your hands free to control the zoom. Try using a remote release to fire the shutter to reduce camera shake. If you don't have a remote cable release try using the self-timer option found on all cameras. A burst of light from a flashgun can help freeze your subject and add sharpness to the image too.
The key to the image is getting the zooming action right. If the zoom is too obvious it may make an interesting image but it will disguise your subject. But if you don't zoom enough it will just look like a normal picture. Even though you can zoom either way most people choose to zoom out.
Once the shutter opens, wait for a while (half to three quarters of the exposure) then in one fluid but quite fast movement, zoom out. That way, you get a get a bit of definition into the subject before you blur it. We're lucky that digital cameras let us see the results straight away so if the zoom isn't quite right, you can re-set and do it again. Of course, your subject and creative aims will change how the shot is taken.
If you want to add speed to an image rather than a burst of light or colour, zooming out then starting a short exposure while you're moving the zoom will help you do this.
A small aperture (around f/22) is needed to allow a slow enough shutter speed and you should use ISO 100 or 200. A slow shutter speed of one to four seconds is needed but that can be tricky with a subject like a stained glass window because of strong backlighting. The need for a slow shutter speed is because it make it easier to time when to start zooming - with an exposure of 1/2 or 1/4sec, that is very difficult to do. If it is so bright that you can't get a slow enough shutter speed, fit a polarizer or neutral density filter, set an even lower ISO if you can or find a less brightly backlit window. When you meter, make sure you do it from your main point of focus.
It may take some practise before you have this perfected but experimentation and perseverance is the key to cracking this technique.