Here is a short video explaining the basic operation of a underground irrigation system.
Usually an irrigation system is quoted/estimated by number of required zones. Roughly $500 to $700 per zone. Price depends on location, logistics of install, permits, regulations, and complexity of the system. You will most likely incur other expenses such as deduct meter and required permits. There is also going to be a minimum charge for very small systems.
The backflow valve is required to keep water from flowing backwards. I.e. if there was a water main break and the public water supply lost pressure. The fertilizer and or any pesticides in your lawn could enter the public water system and contaminate the water supply.
The deduct meter is used to deduct the amount of water you use from your waste water bill. Not necessary if your on a septic system.
The controller is basically the brains of the system. It turn the control valves on and off to which waters the desired zones. It regulates the amount of time each zone is on. Also receives input from the sensors and adjust the system/timing accordingly
The main lines are charged or under constant pressure. Or until the system is winterized. The lateral lines are only charged/pressurized when the control valve is activate.
Zones: An irrigation system waters a lawn in sections. I.e. front, back, sides etc. These sections are referred to as zones.
Control Valve: A valve which is activate(opened) by the controller which in turn waters each zone.
There are different types of sprinkler heads depending on are being irrigated. I.e. rotor heads are used to cover larger areas where as a simple pop up head is designed for smaller areas such as between street and sidewalk. A drip system is used to water your landscape plants
Rain senors simple measure the amount of rain and will adjust the the amount system accordingly. A Freeze sensor will shut the system down till the temperature is safe enough to run the system without incurring damage