The "blurred" effect (sometimes called 'bokeh' I think) is created by using a wide aperture. On a DSLR you can set the aperture and different lens can have different maximum apertures.

I am not aware of a point'n'shoot that lets you set the aperture, but that doesn't mean they don't exist. However, you're limited to what the built in lens can achieve, which is unlikely to be enough to create the blur effect you desire.

You may be able to achieve something similar in photoshop. I've never tried though, and I can't imagine it would look as good.

As for manual mode, the camera's instruction manual should talk about it, so in the shop ask to see this. It may also be obvious by looking at the camera itself.