The key to a black background, is to have less light reflecting off of the background, than off of the subject. You obviously need to set your exposure for the lighting on your subject...you will then want the background to be at least 2.5 stops darker.
This doesn't mean that your background has to be black to start with, it can be white...it just has to be darker than your subject. You can create this by ensuring that the light you have on your subject, is not getting onto the background. One of the most basic ways of doing this, is to have the background be as far away (from the lights) while having the subject much closer to the lights. Another trick is to use 'flags' (something between the light and where you don't want it to go), but it also helps to use things like grids & barn doors on the lights, to keep them constrained to where you want the light.
Of course, using a surface that absorbs a lot of light, rather than reflects it, is helpful. Black velvet, for example, eats a whole lot of light.