Question
I just moved to a home and found out, while diging a trench to direct the water away from the foundation of the house, that I have a layer of clay that ranges from 2 inches to over 7 inches in the yard.  I would like some guidance on how I can break up the clay and get grass to grow.  There are about 15 trees in the yard that were aparently planted before the clay was put down and tilling the whole yard is not feasible.

My main problem is that when it rains the water just stands on top of the ground and does not penetrate the clay layer.  Can I use lime to break down the clay or am I just out of luck?

I live about 35 miles north of Houston, Texas.

Answer
Hi Wyatt, Repeat after me..."Clay is good".  Clay is the soil of choice to start with.  It has good water and nutrient retention but because the particle size is so small, water is slow to percolate through it.  You should have no problem growing Zoysia, St. Augustine or Bermuda lawn grasses in clay soil if the pH is around 6.5 and you are fertilizing and mowing properly and there is sufficient sunlight.
Water standing in an area is a slope/drainage problem, aggravated by the clay but not caused by it.  You may (believe it or not) need to add clay to elevate some low areas or trench to remove standing water.
I suspect the trees are the main reason your grass is suffering.  Most turfgrasses prefer full sun, some will tolerate shade but as the shade increases, the vigor of the grass decreases.  The trees are also the dominant organism in your ecosystem...that's just a fancy way of saying the trees absorb most of the water and nutrients from your soil so you will need to monitor these levels for a successful turf.
Lime may be needed to keep your pH up but it will not significantly effect your drainage.  Since tilling is out, here's a cheap way to solve your problem...
Go to your local drugstore and look at the shampoos. Look for this ingredient:  Sodium laureth sulfate.
You'll usually find it in the really cheap shampoos.  Pour this into a hose attachment sprayer and spray the areas where water stands.  This causes clay particles to not stick together and really improves the drainage of clay soils. Good Luck.