What you need:

Tripod
Camera with a zoom lens (the longer the zoom the better)
Subject you want to zoom (lights are really interesting - I used tea light holders)
Cable/remote release (optional)

What to do:

Place your camera on the tripod and set up your subject in a way that there's ample room in the frame around the subject. It's a good idea to place the subject in the centre.

Set an adequately low ISO as you will be using a long exposure and choose an appropriate White Balance if you're going to shoot in JPEG (you can leave this on AWB as well).

Set a slow shutter speed - anything slower than about 2 seconds; this will ensure that you have enough time to zoom your lens. Of course, try other shutter speeds as well, just for fun!

Choose a moderately large depth of field if you would like the zoom to be sharp. Otherwise, choose a desired f/stop for the kind of shot you want.
Now you are ready! Trip the shutter and being careful not to shake the camera or the tripod, zoom your lens in or out.

Way to go - you've got a really cool shot!

This shot was Zoomed out to 55 mm, f/13.0, 4s, ISO 100, AWB
I tripped the shutter, waited a second or so, and then zoomed in half-way fairly rapidly .