If you water in the evening, the water will sit on your grass and plants all night, which can lead to mold. It’s better to water in the wee hours of the morning, before it gets hot. That way, it’s cool enough that the water can soak in well, but any residual water left on the grass will evaporate as the sun rises.
Time will depend on your soil. Sandy soil drinks water in quickly, but doesn’t hold on to it very long. Clay-like soil absorbs water slowly, but holds on to it for a long time. Loamy soil is the optimum mix of both. One way to test how your soil absorbs water is with a can; cut out the top and bottom and push it partway into your soil, add an inch of water, and check it in half an hour. If it’s gone, your soil is very sandy; if it’s hardly absorbed at all, your soil is very clay-like. If it’s half gone, you’re in good shape.
Optimally, you want to give your lawn an inch of water a week. It’s best to give the water in two waterings of half an inch each; that gives your lawn plenty of water to live on, but also gives it time to dry out between waterings. Before we were on water restrictions, I would water on Monday and Thursday, which left the lawn and garden dry enough to work on during the weekend. If your soil is very clay-like, you may have to do two short waterings on each day, with some lag-time in between, to get the full amount completely absorbed.
Oh yeah, one more thing: mow high. I know people think short, even grass is prettier, but the grass won’t be as healthy, because it’ll have to put more effort into regrowing its leaves rather than getting richer and denser. Also, long grass means more shade at the ground level, which means it’ll be harder for weed seeds to germinate.