Answer: I suspect you have both cool season and warm season grasses in your lawn. The cool season grasses are green in the fall, winter and early spring; the warm season grasses are green in the summer. Right now it sounds as though the cool season grasses have gone dormant. In the winter, the areas that are thin in dry will become lush and green while the areas that are now lush and green will turn brown. Since you're in the California desert, the best way to maintain a green lawn all year around is to overseed your lawn with cool season grasses (such as ryegrass or fescues) in October and then overseed again in April with warm season grasses (such as bermuda). Right now, in the heat of summer, there's not much you can do. Grass seeds will burn immediately after germinating in the heat. So, I'd wait until October. At that time you can rake out any bare areas and broadcast cool season grass seeds. They'll be up and green in 7-10 days.
As for general maintenance, lawns need about one inch of water per week, frequent mowing and feeding in April, September and again in December.
Best wishes with your lawn!
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