There’s not a lot to do here. The light itself is just an on-camera flash that isn’t quite wide enough to cover the same area as the lens. It could even be the pop-up flash built into the camera. If you’re close enough to your subject, you can let flash fall-off do what a narrow flash zoom would do, since the parts of your subject that you’d want dark (if you’re duplicating this shot) will be much further from the flash than the brighter parts would be.
The key to the effect is filtering. You want at least a magenta or minus-green gel on the flash. You can then either use a green or plus-green filter on the lens and just leave the camera at daylight (or flash) colour balance (and this will also work if you’re shooting film), or you can correct the magenta cast from the flash in post-processing, which will also make the background green. Do note that plus-green and minus-green photo/cine gels are designed to work equally but in opposite directions, so there isn’t a lot of manual correction to do. Using more generic green and magenta filters will work, but since they’re not balanced, you’ll have a little more playing around to do afterwards, whether that’s in your raw editor, a pixel editor (if you’re shooting JPEGs), or in the darkroom.
If you get the flash away from the camera, you can still get the same colour effects using filtered flash, but are likely to end up with a much better image otherwise, with your subject having some actual shape to the face, etc.