Cut around the affected area with a spade shovel and then remove the topsoil from the area with the shovel. You should remove at least the top inch of soil.
Fill the area with fresh high-quality topsoil and tamp it down with a tamper. Add additional soil if needed until the soil rests level with the ground.
Spread grass seed over the area. Overlap the seed into the existing grass. This will help blend the new patch of grass with the old grass. There are many different types of grass. If you are not sure what type of grass you have, take a few blades of your grass with you when you pick out your seed. A qualified sales rep will help you determine the best seed to use.
Cover the fresh grass seed with hay straw. This keeps the birds from picking the seed out of the ground and blows away within a few days.
Water the grass seed lightly with your garden hose each day until the seed starts to germinate.