If you want to take a portrait like this without blacking out the background in Photoshop, then there are a couple things to keep in mind. The big idea is that you need to make minimize the amount of light that hits your background. You mentioned the inverse square law, and the distance between the subject and the background helps. But the camera settings and directionality of the light also matter. Let's walk through a few steps, point by point.
First, make sure you're starting with camera settings that ensure true black. There should be absolutely no exposure with ambient light. If you turn off your strobe/speedlight and take a picture, you should get nothing but 100% black. This means turning up the shutter speed, turning down the ISO, or closing down the aperture until everything is pure black. If possible, you want to underexpose the background by a couple stops as well (i.e. close the aperture an extra one or two stops).
Second, place the subject with an eye towards the inverse square law. The intensity of light falls off exponentially as distance is increased. So, you need to increase the distance between the light and the background and decrease the distance between the light and the subject. You need to compromise here a bit, because you don't want your light to be 6" from your subject; but you want to maximize the distance between the subject and background compared to that between the light and subject.
Third, make your light focused. Light radiates out in all directions. A bare speedlight or strobe will shine in all directions. The use of a modifier - like a softbox, a grid, a snoot, or even just a piece of cardboard (a "gobo" more technically) - will point the light at your model and keep it off your background. You want to restrict the ability of light to spread out.
Fourth (and finally), make your light directional. Notice how your example image has a deep shadow on the model's neck and right cheek? This indicates the light is high and to the right. It's pointing down and to the left (and the model is facing up to minimize shadows). The light doesn't point anywhere near the background, and a light modifier (according to the point above) will make sure that no light ever hits the background. If, on the other hand, your key light is on axis you will never be able to get a perfectly black background.
Fifth (and an afterthought), make sure that you're not bouncing light onto a background. If there is a wall just to the left of your model and your light is pointing to the left, it will bounce off that wall and hit your background. Instead, you should make sure that there is an open area (so no light is bounced) or you should set up a temporary wall (basically, a giant gobo of cardboard, whiteboard, or black fabric). Any reflected light could potentially add a little exposure to your background and ruin the shot.
So, let's recap. Start by tightening your exposure to black out the exposure. Then, place the subject so it is close to your light and the light is relatively far from your background. Finally, make sure that the light is tightly focused and that it doesn't point towards your background.