For the light portrait you use a single light on the model, no ambient light and no light on a dark background. Depending on what type of light you use, you may need something to block the light so that it doesn't fall on the background also.
The dark portrait is basically the same, but the light comes more from behind, and the background is lit. It may be possible to light the model and the backgtround with the same light, but it's easier to get the levels right with separate lights.
Using a single light for portraits is considered to be very difficult, so you may need to experiment a lot to get it right. You should use manual exposure, as the high contrast easily throws off the automatic exposure in the camera (but that is true for most studio photo anyhow).
It's certainly possible to do at home with minimal equipment, if you have a suitable background. A directional light and a light meter should help a lot, though.