What you are looking for is called "shallow depth of field" (that is, just little bit in focus and the rest blurred).
There are 3 factors that effect depth of field, with a small point and shoot camera you have to combine all of them if you want to get a visible effect (actually there are 4, but you can't change the 4th):
Focal length - zoom in as much as possible (optical zoom only, digital zoom does not help)
Aperture size - switch the camera to A or Av mode (if it has such a mode) and select the lowest value possible.
Subject distance - your subject has to be as close to the camera as possible and the background has to be as far as possible.
And finally, macro mode - usually the smallest depth of field you can get is in macro mode, obviously you can't photograph anything as big as a person but you may just be able to get a complete face into the frame