>>1710115Spray with herbicide following the directions, looks like you are infested with Bermuda, get rid of it that's the devil's grass.
Immediately after that process plant a mixture of nitrogen fixing legumes like clover for example and some summer crops like pearl millet. Let it grow to about between 1 and 2 feet high, then wack it down to 8 inches, leave the waste on the ground and throw some garden compost on it. Then in the fall spray with herbicide again and plant a crop like winter rye, make sure it's perennial. Do the same things again then plant a mixture of cool and warm season grasses that do well on poor soils, as well as native forbs (wildflowers) and legumes like sensitive briar.
Before you do any of this I recommend getting a free soil test at your local county extension to determine what should be grown and what amendments are needed.
Then you can have the coolest lawn in the neighborhood, only it's not a lawn but a native grassland garden that would be a shame to mow but once or twice a year. You could even get a small dairy goat and some rabbits and chickens stocked at low density or on rotation at medium density to get rid lawn mowing entirely. Until the devil's grass rapidly reinvades and strips your soil of nutrients again with a couple years.
Go to DIY lawns aren't out, better yet go to Google and read websites dedicated to this kind of thing.