In the South late spring to early summer is the best time. Before buying grasses, ask a professional at a garden center or nursery what grasses are well-suited for shade in your area. Rye grasses are available in both annual and perennial varieties. The annual varieties work best as green-manure crops in the veggie garden. The perennial varieties are more commonly used as turf grass.
Perennial ryes can tolerate more sun than fescues.
Use a metal rake to remove any debris or thatch. Spread topsoil or compost on the lawn. A store-bought product that's made from composted cow manure and alfalfa is good. Just toss the stuff onto the lawn to get a light but even layer. Now spread the seed.