Detoxing is really a way of getting the impurities OUT of your body, so taking supplements during a cleanse or fast would not be the best idea, since supplements are usually not natural and can be very toxic to your system, as they are not coming to you in any kind of a natural form, but a processed, extracted, unnatural form.
There are different kinds of fasts and cleanses, it's important to be prepared, and if undertaking something as health-changing as a water fast, be sure it is supervised by a professional.
You may want to look into juice feasting, as a way of giving your body a rest from digestion and extra energy for healing.
http://www.rawreform.com/content/view/271/137
Whichever you do, be sure to maintain a healthy lifestyle of whole fresh foods, actvitiy, fresh air, sunshine etc. or your body will be sure to return to its original state as before the cleanse/fast/detox.