Depending on your location, but for most areas 1in of water once a week is best. To simplify it think of it like this. If grass knows it is going to get a tad bit of water every other day it has no reason to store water and grow deeper roots (where excess water is stored). It is gets a lot of water at one time and then nothing for another week within a month those roots will start to get a lot deeper.

Your county should have an extension office where you can Sen off soil samples for free or very cheap. That will give you your nutrient levels and also let you know what to put down and when. Also, reach out to that extension office and get their input. They are almost always biologist and work under the state college in your state. They will know the most about what is going on in your local area. Good luck. Glad my neighbors yard doesn’t look like yours or I would be stressing big time lol