Cut a triangular piece of turf out of your lawn to check the thickness of your thatch layer. A thatch layer over 1/2 inch thick should be removed, which will also remove the dead grass. Thatch is the brown spongy layer that exists between your soil and grass blades. Rent a dethatcher, and push it back and forth across the lawn to remove the thatch and dead grass.
Rake up your dead grass if you have a thatch layer less than 1/2 inch thick. Throw the dead grass away if you suspect that your dead patches were caused by fungal diseases or pests.
Till the bare areas to break up compacted soil for your grass seeds. Press a screwdriver in the lawn to make a small hole.
Place a soil thermometer inside of the hole to test the soil temperatures. Seed warm-season grass if soil temperatures are around 65 degrees Fahrenheit, or plant cool-season grass seed if soil temperatures are around 60 degrees Fahrenheit.
Broadcast grass seeds over the bare areas. Cover your grass seed with 1/8 inch compost, and water enough to moisten the soil.