Man, where to start. Donald will come along with some excellent advice. First, to rub some salt in the wound without knowing what you did here to establish the grass (LOL, in fun, not derogatory) . This is one of those jobs that pays to put in the time, effort, and material costs at the outset to avoid what you now have to correct. But, (again not knowing what you did/happened) weather can ruin even the best efforts (flooding rain, extreme heat, not enough irrigation). You are in the southern border of cool season grass species, so proper grass choice is/was the first step. Soil prep including proper tilth, fertility, etc. all matters. The light/dark areas in your pic suggest fertility issues. Mid summer is the worst time to establish grass (heat, drought, more weed germination) - you have both broadleaf weeds and crab grass coming in.
Options now? You can
over seed bare areas. Spots still with straw - sprinkle grass seed on, rake lightly with the
leaf rake upside down to work the seed below the straw and irrigate daily. Bare soil areas - kill/remove the weeds. Rough up the top inch with a steel
garden rake, sprinkle seed in, lightly rake with leaf rake to cover seed, restraw, and irrigate daily. Probably should top dress
fertilize the entire area with a low rate of about 1/2 pound nitrogen per 1000 sq. ft.. Use 12-12-12 or whatever to introduce the other key elements (not knowing what the soil test is).
You could rent a slit seeder to over seed if you wish.
You have to wait several weeks after seeding to use broadleaf
herbicide (check the label) to start getting those under control. Just keep after it and hopefully this fall it will fill in and thicken with the cooler temps..
Here's shots of tree/stump removal areas I reseeded last fall
using straw mulch. Then...... and today. (more salt in the wound, LOL) I'm waiting
for the relentless rain to let up and will apply a low dose of fertilizer soon.
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EXCELLENT advice here from your local land grant university:
http://www.uky.edu/Ag/ukturf/lawns.html