How to blur the background of a portrait photo on a Nikon D3200?

I want the person to stand out and the background to be blurred, I'm sing a AF-S NIKKOR 50mm f/1.8G lens

Fill the viewfinder with your person (head and shoulders), set your lens aperture to about f/4 (sharpest aperture on that lens) and focus on the persons eyes.

Shoot outdoors in the shade with the white balance set to shade.

Indoors, you will need some very bright lights like 500 watt work lights and with the ISO elevated to about 3200 ISO so your shutter speed is fast enough to prevent blur caused by camera or subject movement (1/250th second would be a good shutter speed -- or faster)

This is a simple case of knowing about depth of field which can be found from many sources. In this case your best option is to use the maximum aperture of 1.8 and focus on the eyes for best definition. If the person's body is out of focus for your needs then decrease the aperture (remembering to decrease the speed in compensation) until you achieve the level of sharpness that suits.

Learn how aperture, focal length and camera-to-subject distance relate to depth of field.

Larger aperture = Shallower DOF.

Focal Length - Longer focal length = shallower DOF. (I know you're using a prime)

Camera-to-subject distance - THe closer you are to your subject, the shallower your DOF will be.

To maximise the 'selective focus' effect you need a narrow DOF;-

The closer you are to the subject the narrower the DOF.

The wider the aperture (low f number) the narrower the DOF. If your very close to the subject using f1.8 DOF may be too narrow, if you want both eyes in focus on a 3/4 view for instance.

There's a third criteria, the larger the sensor the narrower the DOF will be, but as that can't be changed the two controls you have are aperture and distance from the subject.

Obviously having the background some distance behind the subject helps too.

Focal length only alters how close you are to the subject to frame the shot, take the same frame with a telephoto lens or with a wider lens and DOF will be exactly the same at the same aperture.

Make sure your camera auto focuses where you want it, usually the eyes, and your lens will have a minimum focusing distance (1.48ft for your lens)

http://www.dpreview.com/...f1p8#specs

Here is a website that shows you how to do it, using a DSLR and even a compact camera. While a compact camera will not be as easy, or the effect as drastic, it shows that even a compact camera can be used.

http://www.althephoto.com/concepts/selectivefocus.php

It also debunks the myth that you need a fast lens.

And I disagree with Screwdriver; focal length does matter. In fact it is the most significant variable, and is more important than aperture. The effect of focal length is why you can get some effect using a compact camera.

It is all in technique.

Shoot in aperture priority mode, and use f/1.8 to about f/2.8 as your selected aperture.
Get fairly close to your subject, and focus on their eyes.
There you go.