How to shoot or edit a image to have a background blur effet?

Answer 1

For an edit treatment, try this tutorial...

Answer 2

The image must be shot with a large lens opening, which gives a shallow depth of field, so that focusing on the people or other objects of interest leaves the rest out of focus.
If arguing with an automatic camera one opens the lens on a aperture predominant camera (and the camera makes the shutter opening quicker) or the speeds the shutter on a shutter speed predominant camera (and the camera opens the lens.) On a manual camera, normally the shutter speed is set as high as possible and the lens is then opened (usually much easier than setting speed) to set exposure. On some cameras with some film on a bright day, it simply isn't possible to get a shallow depth of field (800 speed film in a camera with a 1/500 second max.shutter would over expose any shot wider than about f:8 which has a pretty good depth of field.)