Turmeric is a great herb for healing the digestive tract and aiding the liver in detoxification. Many herbalists postulate that improved liver detoxification helps to purge the body of toxins. These same toxins if not eliminated through the liver often come out via the skin and can manifest as acne, psoriasis or eczema. For internal use you may want to start with about 500mg-1000mg a day. Some people can get loose stool if they take too much, so start slow and work up to the full dose.
In addition, if you take it at the same time as a fat containing food or supplement you will greatly increase the absorption. I recommend taking it with fish oil as this will also be very beneficial for the health of your skin.
Turmeric does have potent anti-inflammatory actions and would likely help to reduce the inflammation on the skin if applied topically.