For an excellent primer, Bonita, including selecting the right grass, see this publication from University of Georgia Cooperative Extension:
Don't leave out the step of getting a soil sample.
Grass won't grow very well on clay. As with any plant, the deeper the roots, the healthier the plant. On clay, grass roots only penetrate a couple of inches, making the grass very susceptible to drought damage....which leads to weeds in the bare spots.
Add organic matter to clay soil and till it six inches deep.
Add Zoysia plugs. They are drought resistant and provide a low maintenance thick grass. Been growing mine for 20 years and never water it.