Step 2: Kill everything
You can kill the grass with chemicals like Roundup or Killzall. But if you hate the idea of using chemicals and have a large area, rent a sod cutter to remove the lawn surface. Or kill the grass by blocking out its sunlight with black poly film (4-mil or thicker) secured with rocks or stakes. Remove the poly when the grass is dry and brown (two to three weeks or longer, depending on the weather).
Step 3: Remove the dead stuff
Step 4: Improve the soil
Don't think you can fix bad soil just by adding a few inches of black soil on top of the old. Instead, spread the conditioners, recommended by the soil analysis, across the entire lawn. Then rent a tiller and till them into the soil to a depth of about 5 in.
'Adding good-quality black topsoil over bad soil is like putting chocolate frosting on a stale cake?it doesn't fix the underlying problem.'
Bob Mugaas, Turf Expert