How to take portrait photos like this? Background defocus? Nikon d3000?

with a nikon d3000!

Narrow depth of field

and a basic knowledge of cameras and lenses…

Get close to the subject and use the widest aperture you have, a wide aperture lens (50mm f1.4 for instance) exaggerates the effect.

It's called shallow depth of field.

If all you have is the kit lens, then shoot at 55mm at the widest aperture (f5.6) - that will give you the shallowest dof that lens is capable of.

Alternatively, get a 50mm f1.8 prime lens (Nikon's cheapest lens, around £100). You'll need to manually focus it though on your D3000.