These are the steps to renovate a lawn by killing the existing grass and establishing a new lawn:
Mid-August, spray the bad lawn area with Roundup.
About a week later do a repeat spray of Roundup on any areas you missed.
A week later mow your dead grass as short as possible removing the clippings as you mow. Rent a Dethatcher (also known as a Power Rake) and run it over the dead lawn in two directions. Set the machine low enough so that the blades are touching the soil. Rake up the dead grass and add Scotts Turf Builder Lawn Soil to any low spots.
The next day rent a Slit-Seeder to seed your lawn with a seed blend for your situation. For the best grass seed, go with one of the Scotts Turf Builder Grass Seed blends rated for Sun, Sun/Shade, Dense Shade, High Traffic, or Heat-Tolerance. I am a big fan of Scotts Turf Builder Grass Seed Heat-Tolerant Blue Mix.
Spread Starter Lawn Food for New Grass the same day you seed.
Water a couple of times a day for several weeks.
Mow your new lawn at around 2-1/2 inches.
About a month after seeding, feed your new lawn with Turf Builder.