Rake and remove the dead grass and debris from the bare patch.
Use a spading fork or cultivating tool to loosen the soil in the bare area.
Incorporate 2 to 3 inches of compost into the prepared area.
Smooth the area with the back of a rake until the new soil is level with the surrounding area.
Seed thickly and evenly (taking care not to overcrowd the seeds or jumble them on top of each other). Incorporate the seeds into the soil gently, using the back side of the rake.
Cover the seeded area with a thin layer of fine compost or other organic matter to act as a protective mulch.
Water gently with a fan nozzle so you don't wash the seeds away.
Protect the area from birds if they are a problem. Insert 1-foot-long wooden stakes into the ground surrounding the perimeter of the patch, keeping the stakes 10 to 12 inches apart. Tie red Mylar flash tape to the stakes. This will frighten birds away from the seeded area.
Keep the repaired area moist until the seed germinates. Once the new grass is established, resume regular watering.