If you want to take portraits like you see in magazines where the subject stands out from the background, you'll need to pay attention to aperture. The smaller the f-number, the larger the aperture and the more softened the background will be. Choose larger f-numbers to stop aperture down for a sharper background.
To control background softening, choose "aperture-priority auto" mode. You choose the aperture and the camera will automatically adjust exposure for optimal results.
Background softening is also dependent on the lens. At the angle of view of most standard lenses, the background is nice and sharp; if you want to soften the background, you'll need a lens with a longer focal length (a telephoto lens). Magazine photos produce their delicate background softening through clever combinations of aperture and focal length.