How to turn on my irrigation system
First thing to check: is there (or was there) a well?  If your sprinkler system is attached to a well, then this is the first thing to check.  Make sure it's on and operating correctly.

If it's not attached to a well, then it's just a matter of tracing the pipes, possibly from each end.  Locate the main shutoff in the house and any lines running to unknown locations, particularly back outside.  Make sure all valves are open.  Then from outside, trace the line running back into the house and check if there are any access panels in the path that could be hiding a valve.

Finally, just an obvious check, check your breakers and make sure the system doesn't have a rain switch that has been activated.