See the article on zones and the water use of each zone. If you take the amount of heads on the zone and multiply it by the GPM and then by the number of minutes you run the zone, that will give you the total amount of water you use each cycle. If you add that up and calculate your city's water rate, that will give you the cost to run your sprinklers.
7 Zone system
3 Rotor zones (4 heads each zone) = 12 GPM/Zone
4 mist zones (10 heads each zone) = 10 GPM/Zone
Each rotor zone runs for 20 mins. per day 6 days per week
Each mist zone runs for 10 mins. per day 6 days per week.
Rotors: 60 mins/day x 12 GPM = 720 Gallons Per day
Mist: 40 mins/day x 10 GPM = 400 Gallons Per Day
Total Day = 1120 Gallons
Total Week = 1120 x 6 = 6720 Gallons Per Week
City water Rate is $5.00/750 Gallons of water
Total Weekly Watering Cost is roughly $45
There are a few factors that may effect these numbers such as nozzle size on the heads, but this is a good rough estimate of how it works.