Walk the grass lawn area with a sod stripper to remove old grass and weeds. Although your soil would benefit from the vegetation of the grass, you cannot risk tilling in weeds that might pop back up later. Dispose of the stripped lawn material in backs or possibly a wooded area or compost.
Test the soil with a soil test kit. Follow the directions on the package to collect soil and test its pH. You need a level of between 6 and 7 for grass. This is slightly acidic.
Cast fertilizer on the soil to adjust the pH level if it is needed. Follow directions on the package as to quantities based on the size of your yard. Use a garden spreader to cast the granules over the yard area.
Pour organic material on the soil. Use mulch, compost, peat moss or manure. Use about 6 cubic feet total material for every 1,000 square feet. You can use one type of material or a mixture of several. Rake it out evenly over the lawn.
Till the soil with a tiller down to a depth of 6 to 8 inches. Walk behind the tiller and push it along like a lawn mower. When done repeat the process in rows perpendicular to the first tilling. This breaks up the soil, incorporates oxygen and mixes in the organic material.
Rake the soil out smooth with a rake once it is all tilled.