First, choose a scene that you think will look good with this effect. City lights and skyscrapers work well and so do flowers, but there are lots of possible subjects. Set your camera to a slow shutter speed (1/8 of a second with slower being even better). This is where the tripod comes in handy. Since you're working with a slow shutter speed and zooming the lens the possibility of blur from camera shake is very high. A stable shooting platform will reduce the effects of camera shake.
Before trying the shot, make sure to practice a few slow zooms. The smoother you can make the zooming motion, the better the result will be. Push-pull zooms are easier to use for this technique, but twist ring zooms can also work well with some practice. Make sure you make multiple efforts since it can be hard to get the technique just right without practice. Also, start the zooming action before tripping the shutter. If you're photographing a human being, caution them to remain as still as they can since the slow shutter speed will cause any movement by the subject to result in movement blur.
If you don't have a tripod, try to find some kind of stable surface like a table or wall to brace the camera on since that will help keep the camera steadier.
For a different kind of effect, try combining this technique with dragging the shutter. Your flash will fire at the beginning of the exposure and produce a strong start to the image while the ambient light will register a less pronounced zoom effect.