Rent a power rake from a garden supply store and place it at one edge of the damaged lawn. Turn the rake on as instructed by the user instructions and set the blade depth to between 1/4 and 1/2 inch deep. Push the power rake over the lawn in side-by-side rows to aerate it and prepare for seeding.
Fill a seed spreader or fertilizer spreader with the same variety of grass seed that is already growing in the lawn. Set the dispenser rate to 1 to 2 lbs. for every 1,000 square feet of lawn. Push the spreader over the lawn in side-by-side rows to dispense the seeds, just as you did with the power rake.
Rake the lawn gently with a standard leaf rake to push the grass seed down into the soil by about 1/4 inch. Some of the seeds should still be visible on top of the ground.
Water the entire lawn with 1/2 inch of water immediately after spreading the seeds. Afterward, water daily to keep the soil moist for three to four weeks or until you see new grass blades sprout up.