Almost all public land sites have a registration to hunt there. You'll need to go to the park during business hours and complete a form. They will give you a tally sheet / permit that you need to display in your vehicle. The hunter fact sheets are a valuable resource. They tell you about any limitations, restriction, parking info, season dates, no hunting areas, etc...One thing to be aware of, some of the Pheasant release parks have a limited or shortened bow hunting season.
http://www.dnr.state.il.us/lands/Landmgt/hunter_fact_sheet/
You will need to have your hunting license, habitat stamp, and permits.