If you are using something like a black theatrical curtain, which is very common in video production, you are going to want to position the lights and the subject just perfectly. If you want it to appear as though a person or object is against a black nothingness, then you want to keep the light away from the background somewhat. Bring the person several feet away from the background while keeping the black overwhelming the frame.
Now, use the three point lighting set up with a light on one side of their face, a fill light on the other and a backlight on the back of his/her head. Do not use a background light at all. Bring the lights closer to the person than normal, especially the backlight. Now, the person will likely be too bright, or “hot,” so you can just reduce the iris until they look appropriate. They will now look correctly lit while the background will look like pure blackness.