Answer: If the water is running off, then it is being applied too fast. If applied more slowly over a longer period of time it will be able to soak into the soil rather than run off.
You can help the water to soak in by doing core aeration followed by a top dressing of compost. This will allow both air and water to infiltrate the soil better. The soil improvement should also help your grass grow better.
The other big step to take is to run some basic soil tests and check the soil fertility and the soil pH. Then fertilize and/or apply lime as indicated by the soil tests. Getting the correct pH will help the lawn utilize the fertilizer and also discourages some weeds. As your grass grows thicker it will crowd out weeds as well.
Make sure you are mowing correctly to encourage better lawn grass growth. Mow high at three inches. Mow often enough that you do not remove more than one third the grass height when you cut it. This can mean mowing more often than once a week when the grass is growing fast in the spring for example.
Bare patches can be caused by insects or disease or simply poor growing conditions. I would suggest you consult with your local Penn State county extension to analyze why the bare patches are occurring and based on knowing that, determine how to proceed. I hope this helps you trouble shoot.
Q&A Library Searching Tips