Answer: Unfortunately, dogs will ruin a lawn by running on it especially in wet weather. The best way to have a lawn is to create an area for the dogs to run and play, and then grow lawn on the remainder.
To establish a lawn, you should run some basic soil tests to see if you need to fertilize or add lime. To prepare the soil, remove existing weeds and grass, loosen it down about six inches and add organic matter such as compost. Work in the lime if tests show it is needed. Then level the area and rake the surface smooth. At this point you would lay the sod or seed. Sod is by far more expensive but gives instant results.
To seed, spread grass seed lightly as directed on package. Rake again to lightly cover the seed. Water immediately, and then as needed to keep the area slightly moist. You may need to cover the soil with a light layer of straw to help keep the ground shaded and moist. The best time of year to do all this is late summer to early fall.
For now, you might try a quick overseeding or seed the worst parts to try to cover the ground to hold down the dust this summer. Mow often enough that you never remove more than one third the grass height at a time. This will help the existing grass be as healthy as possible. You should also run the soil tests and fertilize and lime now as indicated by the tests. If the lawn recovers, it may not need to be fully renovated this fall, you may be able to overseed it instead which is much easier.
Your local county extension should be able to help you with the soil testing and interpreting the results, and should be able to help you develop a lawn care and maintenance plan based on the type of grass you are growing and the conditions in your yard.
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