Quick answer: About 1 inch of water a week, rain included, applied in one or two deep sessions rather than a little every day. Water early in the morning, not in the evening. Warm-season grass (Bermuda, Zoysia, Centipede, St. Augustine) can handle more missed watering by going dormant; Tall Fescue needs more consistent water, especially through summer.
Why deep and infrequent beats daily
Watering a little bit every day keeps the top inch or two of soil damp and encourages roots to stay shallow, right where they dry out fastest in a hot spell. Watering deeply but less often pushes roots down into cooler, more moisture-stable soil, which is what actually builds drought tolerance over a season. One or two deep waterings a week that add up to about an inch total, including any rain, beats a daily light sprinkle almost every time.