How would you do this on a Nikon D3000?

Sequence shooting.

You can find out how in your user manual, but you will have to merge them all together in photoshop or another editing programme.

Have the camera on a tripod so the frame doesn't move between shots. Put the camera into continuous speed shooting mode see p. 53 of the manual. It will shoot at 3 frames per second (fps).

You then combine the images in layers in Photoshop.

Those shots were on a Canon 20D, 5 frames per second. The D3000 will do 3, so if you did the same setup, you will have the shot with only 3 images in it.

As other have said, tripod, photoshop, layers.