Till the area which will be planted. Rent a garden tiller from a local home center or plant nursery. The best time to till is in the spring, preferably after a rain when the ground is soft. Tilling flips over the top soil and exposes the richer soil below. Turn over the top inch.
Take a soil sample to a local agricultural laboratory for a soil test. The Department of Agriculture's local branch office (see references) will be able to recommend a lab in the area.
Use the lab's recommendations to add fertilizers or soil enhancers to the soil. Red Dirt soil often needs fertilizers such as lime to enrich the soil. Add these fertilizers according to the instructions. Lime, for instance, is most effective when added six months before seeding.
Spread organic compost over the lawn area. Use compost from a home compost-pile which has been composting for at least six months (organic material from the house mixed with leaves and dampened periodically) or purchased at a plant nursery or garden center.
Work the compost into the soil with a tiller or a rake.
Add the compost a few days before seeding.
Seed the lawn.
Walk around the lawn area and scatter grass seed by hand.
The best grass seed choices for red dirt soil are bermuda, fescue, centipede and zoysia.
Water the lawn area as much as possible.
Water every other day at a minimum. If possible water twice a day, at least for the first several weeks.