You can hunt on your own land or on the private land of another in Illinois, as long as you have permission from the owner of the land. Prior to hunting, however, you must have the owner of the private land on which you wish to hunt fill out a Land Access Permission Card. You should carry this document with you whenever you hunt on private land. There are also a number of public hunting areas that are managed by the Illinois DNR. Visit the DNR's website for an up-to-date list of the state's public hunting areas. Many of these areas require a site-specific permit before you hunt. Visit the DNR website to get a windshield card to hunt at a designated area.
Check out these Sheldon, IL Hunting resources:
