A friend of mine worked on a grounds crew, and we discussed this topic a few years ago.
Once you have a compact, graded surface (your clay), dump approximately 6-8 inches of #2 stone, which is then topped with quarry dust and packed down firm. This apparently provides a stable, yet porous base, allowing your topsoil to drain.
According to my buddy, this is where you will shape the surface of your green, by providing the undulations/breaks, etc.
You will then top your green with 10 inches of the finest topsoil that you can afford. There are a number of varieties of grass that work well in different areas of the country.
For drainage, remember: the slope of the clay should reflect where you want the water to drain. Good luck.