The best way to tell if a stone is a real diamond or a cubic zirconia is by using a pen-sized probe called a diamond tester. When looking at the surface of the stone, a real diamond will be free from scratches and the diamond will refract a gray light.
Another way to test a stone to see if it is a real diamond is to try to scratch glass with it. A real diamond is hard enough to put a scratch in a piece of glass, but a cubic zirconia will do nothing. With enough pressure, the CZ gem could actually break under pressure.