1) Check for scratches on the surface. Since diamonds are the hardest known natural material, they do not scratch easily. Ideally, a real diamond should not have scratches on its surface. This will be the first check to test for a real diamond.
2) Breathe on the stone. Real diamonds don't retain heat and so if you breathe on them, they should clear up almost instantly. American diamonds will stay cloudy for a longer period of time as they do retain heat.
3) Use a newspaper. Place the diamond on a newspaper. Real diamonds refract a lot of light, making it nearly impossible to read the letters through it. If you are able to read the letters on the newspaper through your diamond, then it is probably an American Diamond.
4) Weigh the stones. A cubic zirconia is about 50 percent heavier than a real diamond. These methods should help you quickly differentiate between the two stones by yourself, but it is always best to verify with your local jeweler given the huge disparity in prices. This way you're doubly sure that you received what you paid for.