When installing a new lawn, the importance of soil preparation cannot be stressed enough. Proper grading, tillage, and nutrition are essential to the long-term success of your new sod.
Clear the site of all building materials (wood, bricks, cement, etc.) as well as any buried stumps, rocks, stones, or other debris that are larger than 2-3 inches in diameter.
Rough grade the entire area to eliminate any drainage problems on the entire property. This would include sloping the grade away from building foundations, eliminating or reducing severe slopes, and filling low-lying areas. A tractor mounted blade and/or box are most often used for rough grading, but if the area is small, it can be done with hand tools.
Initial tilling to a depth of at least 2 inches should be completed prior to adding any soil amendments. This will control most annual weeds, alleviate subsoil compaction, permit a bonding of the topsoil to the subsoil, and improve root penetration as well as air exchange and water movement. If no new topsoil is going to be added, you should try to achieve 4-6 inch tillage.
Add good quality topsoil (if needed) to achieve total topsoil depth of 4-6 inches, after firming. To the extent possible, practical, affordable, and available, incorporate humus (fully decomposed organic matter) into the topsoil. Many local companies offer nutrient-rich compost/topsoil blends.
Test the soil pH with a chemical soil test to determine if any pH correcting materials are required. Acidic soils (pH of 6 and below) can be improved with the addition of pelletized lime. Alkaline soils (pH of 7.5 and higher) can be improved with the addition of sulfur or gypsum.
Finish grade the entire site, maintaining the rough grading contours and slopes, with a tractor-mounted box blade or pulverizer for large areas or a heavy-duty rake for smaller areas. Final grade should be approximately 3/4 below driveways, sidewalks, etc.
Apply "starter fertilizer" that is high in phosphate ("P" or the middle number on a bag of fertilizer), at the recommended rate. Ideally, rake the fertilizer into the top 1-2 inches. Organic fertilizers make a good choice for this application.
If your soil is loose and fluffy, you may roll the area with a lawn roller one-third full of water to firm and settle the surface. Low spots revealed by this step should be filled to match the surrounding grade surface. If time permits, allow the area to settle further with rainfall or by applying irrigation.