That's not how crab grass grows. But it is how St Augustine grows. You might live in a micro climate that supports St Aug. Obviously you perceive it as a weed so let's get rid of it. First lets be sure that's what it is. Do the ends of the grass have blunt tips or pointed tips? Blunt means St Augustine. Pointed means...not St Augustine ;-) Since it is a grassy weed in grass, normally that would be a problem to get rid of; however, St Aug, if that is what it is, has some weaknesses you can exploit. The first is that it usually dies from broad leaf weed killers like Weed-B-Gone.

Does your soil become soft after a rain? Or does it feel rock solid underfoot after it rains? If it is soft after watering, then that's what you want. Ignore the idea that it might be clay. All you care is that the grass grows in it. If it does stay solid after rain, we can address that.

Here are the basics of lawn care.

Watering
Water deeply and infrequently. Deeply means 1 inch all at one time. Infrequently means different things depending on the temperature, humidity, wind, grass type, etc. For you it means watering only once per week in the hottest heat of summer. This time of year you should be watering nor more than once every 3 weeks. ONCE. But if you water a full inch at a time, once is plenty. I suspect watering is your main issue.

Mowing
Mow at your mower's highest setting. There are exceptions for bermuda, centipede, and creeping bentgrass, but you don't have those.

Fertilizer
Fertilize once in the late spring (Memorial Day), once in the early fall (Labor Day), and once again after the grass has stopped growing in the fall (Thanksgivingish).

Overseeding
If you have a fescue lawn that has thinned out, then you should overseed in the early fall. Early fall for you was 3 weeks ago, so get started!! The idea is to get the grass up and growing this time of year so the roots are strong enough to survive through summer in 2015. If you have something other than a fescue lawn, it should not need to be reseeded. Simply following proper watering, mowing, and fertilizing should solve 99% of the issues.

Thanks so much for your reply. The picture is actually of sod that I put down that didn't take, except for where I put down a couple inches of topsoil as a test. I'm going to be seeding this weekend and putting down weed killer as well? I'm definitely a novice when it comes to this, but the ground I'm working with almost had the seed rinse off after watering. Even if it rains it stays rock hard and the water just runs off like a drain.

Thanks again for your reply!