When shooting in a studio one of the frequent demands is to create a perfect white background or a perfect black background. Whilst small variations can be corrected using software such as photoshop this will frequently change the subject as well. Also fine detail such as hair might be lost. It is always best to try to light your subjects as close as possible to the final image and not rely on photoshop. You will however require a flash meter to get the settings right, otherwise there will be a large amount of trial and error.
For this situation you will not only a light for the subject but also lights to illuminate the background. The backlight should be set up so that it provides a diffuse light over the background that will be in shot. There are various ways of achieving this, the easiest method I have found is to set up some cheap flash units that having an optical firing system.
When you have set up all the lights, turn off the studio flash which will be for the subject or model you are shooting. Then fire the background flashes and make a measure of the lighting. The figure you get, say for example f32, will be to produce a neutral grey. To make this pure white you need to over expose by 2 or 3 stops, so adjust the exposure accordingly (f11 for the above example).
Now turn off the backlights and turn on the models light and adjust the light output so that you get the correct amount of light for the chosen exposure.
Now turn on all the lights and do some test shots. You will probably have to make some minor adjustments to the exposure depending on the actual photographic studio set up you have. How confined the space, what color the walls are, how how the ceiling is will all effect the amount of reflected light and consequently the exposure and light levels you need. You will however be in the right ball park.
One frequent problem to look out for is the background having subtle variations from white to light grey. By repositioning the backlight or backlights and perhaps adding additional lights or diffusers this can be corrected. Don't fall into the frequent trap of trying to increasing the backlight massively so you have a 3 stop over exposure in the darkest area of the background and a greater over exposure say 4 or 5 stops nearest the light. This will create problems with lighting the subject, especially if you are working in a confined space.
A black background for photography is actually far easier to achieve than a white background. There is one simple rule that will ensure that your blacks and jet black if you follow it. Make sure your background is at least twice the distance from the light source than the subject is. It really is that simple. If you have the space and there is little reflected light you will also be able to turn a charcoal grey background cloth into a jet black one by moving the background further back.
By using these two tips you will find that your photography is so much more enjoyable - when you finish a photoshoot you will find that your images are perfect without having to resort to changing levels or curves in photoshop. Above all experiment and enjoy your photography.