The first thing you should now is that you can't clone someone by doing this. You need to find some way to keep it supplied with oxygen and a energy source(food). It still probably won't work. People put organs in ice to delay the inevitable expiration of the organ. Medical science can't keep it alive.
You can keep a cut skin or tissue alive and growing by making sure that there is exchange of oxygen, carbon dioxide and nutrients in the tissue. You should also make sure that there is constant blood supply. A tissue is always delicate and will need special treatment. Consult a lab technician for more details.