Let the old lawn die completely. You can use a herbicide, but to prevent lingering damage to the soil the best way is to simply stop watering it until it becomes brown and dry.
Till the old lawn into the soil to a depth of about 6 inches. This automatically adds organic matter to the soil and also aerates the ground so that the roots of your new lawn will have room to breathe and grow.
Add peat moss (for the right amount for proper coverage, see the instructions on the bag) and till the lawn area again.
Rake the lawn area, removing any remaining clumps of old lawn as well as other obstructions like chunks of soil or rocks.
Sprinkle on granulated lawn fertilizer (again, for the right amount, follow the instructions on the bag) and then rake again, this time to a smooth, level surface.
Water thoroughly and let sit overnight. Lay your sod when the soil is moist, but not wet, to a depth of about 6 inches.
Lay the first patches of sod--they generally come in square yards, weighing about 50 pounds each--along the edge or along a walkway to establish a straight line. To fill in irregular areas, cut strips of sod with a knife or putty knife. Press each piece of sod tightly against the adjacent piece and then press down lightly with your hands so the entire square comes into contact with the soil. Continue until the entire area is covered.
Go over the entire area with a lawn roller, filled with water. This further ensures that your new sod is in close contact with the ground below, which is critical for new root growth.
Water thoroughly as soon as the sod is in place and water daily for at least three weeks. Your water needs to soak through not only the new sod, but also the ground below, so make sure you apply at least 1 inch of water a day to the entire area.