Obtain a soil analysis from your local university extension. A soil test will give you accurate information about your soil's composition and texture, as well as pH and nutrient levels.
Till the soil with a rotary tiller. This will open up the soil and allow you to better incorporate your soil amendments. Avoid tilling clay soils when they are wet.
Incorporate organic matter, such as peat, compost or manure, into the soil. Organic matter increases the amount of space between soil particles, which will make your soil more porous and less likely to compact. Spread 1 to 3 inches of the organic matter over the soil and then incorporate it at least 6 inches into the soil. This ensures that it is available to the root zone of your grass. For an entire lawn, it is probably most effective and convenient to use a rototiller to incorporate organic matter, although hand incorporation may result in less damage to soil structure. If you do incorporate by hand, use a spading fork to mix the soil thoroughly without damaging it with excessive shoveling.