I've got a forerunner to this camera and the explanations above cover your situation well. In order to get that blurred effect there are a couple of things that you are limited by technically - your lens (it's attached) and the ISO (or how sensitive the camera is to light). The other factor is the distance between your subject and the background you are trying to make appear blurry.
To ensure that you are shooting at the most open aperture for the lens I suggest putting it into 'A' mode as Bulevardi suggested. The camera should adjust the rest of the settings to ensure an appropriate exposure.
The other thing to do is stand your model away from things in the background eg. walls etc. If you want to add another component try shooting in about 100-200mm range. There's debate about the most flattering focal length for portraits but this will give you a good wide open aperture still and help to flatten the background and blur it.
The suggestion of Portrait mode is a good one. It basically puts the camera into Auto mode for selecting a small aperture, but you lose a little bit of control as the camera is still adjusting everything automatically it is just biasing itself to how it makes those decisions to a portrait setting. Personally I'd stick with 'A' mode and playing some more to discover what you like the most.
Just as a note, the relationship between ISO, aperture, lens length and shutter speed are usually covered by most basic photography books. Some are better than others but once you understand these well, then you will find you can get the camera to do what you want it to more easily. I'd grab a book from the library or look online for something friendly when you have the time.