I've seen quite a few P&S shots that had shallow DOF.
Try putting the camera in M (Manual) mode or Av (Aperture Priority) mode and then set the camera to it's smallest aperture setting (largest aperture opening). You can even try using the Portrait mode. Zoom the lens out and then get fairly close to your subject. Make sure that the subject/object isn't close to the background. Use a tripod if necessary.
Also,
see this tutorial for more info.