The easiest answer to this question is – only when it needs it and then continue until the water starts running off.  The key to irrigating turf is to water deeply and infrequently. This will create a deep root system that can efficiently use water and nutrients in the soil. Watering for short durations every day will create a turf that has a shallow, weak root system (with the exception of brand new turf that has not yet established itself). Promoting this type of growth will set your lawn up for failure during stressful periods.

You can tell when your lawn needs water when it changes color, when you start leaving footprints for an extended time, when the blades start to wilt, or when a screwdriver stuck in soil comes up dry.  By watching for these signs over a period of time, you will begin to see a pattern – on average, how many days after a rainfall, or an irrigation cycle, does your lawn begin to show it need water.  Here in the Midlands during the heat of summer, you will usually find that the lawn needs water around twice per week.
Many sources indicate that 1 to 1-1/2 inches of water per week is required during the hottest and driest months in this area.  (This is determined by measuring the total evaporation of water from the soil plus the actual usage of the water by the plants – transpiration). 

To determine how long  to run each zone, you must first find out the application rate of the sprinkler nozzles in each zone.   The easy way is to look up the rate on the manufacturers website or catalog, or call an irrigation distributor.  Or, you can place six to eight straight sided cans in the zone and run for 15 minutes.  The average depth of the water in the cans multiplied by four is the application rate in inches per hour.  You may have to perform this test for other zones that have other type of sprinklers.  You can then calculate how long to run each zone for the number of applications per week determined above. 
For example, if your sprinklers average 1” per hour, and you see a need to run twice per week, you need to set the controller for that zone to run for ½ hour to apply 1” of water per week.  If this application rate results in excessive run-off because the water cannot soak in fast enough, run for 20 minutes three time a week.