Irrigation systems are very reliable and need little care for the most part. There are a few things that will help keep your system up and running.
The first thing is make sure you water on the correct days and times. Odd address homes water on Wednesday and Saturday, even address homes water on Thursday and Sunday. All watering is to be done before 10:00 and after 4:00. Check when your system is on that all the heads are working and spraying where they are supposed to. Heads that spray onto concrete driveways or sidewalks should be adjusted. Check that no spray is hitting your home also. Check to make sure that all the heads clear your turf and if not you may need to raise them. Some systems will be fairly easy. Just take a shovel around the head and carefully dig next to it and if it is on poly pipe, a black hose, you can usually just lift it up and repack the dirt. If yours is not on poly pipe, you will need to either get taller heads or add an extension to clear the turf.
Be sure to run your system. The valves especially can have trash get in the diaphragm area and gum it up or the valves get sticky and want to not come on or stay on and will not shut off. This seems to happen more with reclaimed water, but can happen to any system. Try to run each zone for a little bit every couple weeks just to keep things working.