You're going to need to use a longer focal length coupled with a wide aperture (lower number). In portrait mode the camera should set a wide (hopefully the cameras widest) aperture by default, but you still need to use a longer focal length for the subject and make sure they are a decent distance from the background. If the subject is too close to the background the background will still have too much detail. Basically, if your subject is just two or three feet from the background and you're just two feet away using a relatively short focal length, it ain't gonna happen 😉 . A wide aperture gives you the limited (shallow) depth of field, the longer focal length gives you the narrow angle of view and the distance of the background ensures that it's well away from the plane of focus (focus falls of with distance from the focal plane).
