Contact your county agricultural agent and he'll probably mail you a packet of information that's made for your area. That will let you know what grasses grow best in your area.
According the the state of Tennessee, the single best thing you can do is mow. Mowing keeps the weeds low enough for the grass to take hold. Because of this, you might not need to spray a weed killer.
While it's late, I'd sow seed right now, planning to hit it again in the spring.
Mow it low, harrow it lightly, seed and fertilize it. Do the same thing again in the spring, and plan for it again each and every fall.
Submit a soil test to see what the land needs is another good idea.
Again, mow, mow, and mow.