Clay soil is hard to work with because of the fine particles it contains. Clay does not allow for good water drainage or air flow. Grass roots will drown during periods of heavy rain. Grass seeds will also have trouble penetrating clay soil when it dries and hardens. Adding organic material to the soil to amend its drainage capabilities and allow maximum air flow to to roots will produce a healthy, lush lawn.
Break up the clay soil using a rototiller (for large yards, it is recommended that you use a contractor with heavy equipment to break up the soil). The rototiller needs to go to a depth of 8 inches. Cover the yard with 2-inch layers of wood chips, grass clippings, leaves, straw, and peat moss. Till the area to mix the amendments into the clay soil.
Dust the yard with lime, creating a fine white coat. Cover with 2-inch-thick layers of compost, manure, and sand. Till these amendments into the soil to mix thoroughly. Test the soil for drainage by picking some up in your fingers. Roll the dirt between your fingers, if it forms a long flat layer without crumpling, add another layer of amendments. Till all amendments into the soil.
Sow grass seed over the yard. Cover the grass seed with straw. Do not walk on the yard until the lawn has taken a firm hold and the grass roots have had a chance to completely develop. Leave grass clippings on the yard to decompose and add to the organic material in the soil.