In addition to a hunting license, you need a habitat stamp (only cost about $5). On public land, you usually have to sign in and out at a check station, and when you sign out, there's a spot to list your harvest, but you don't have to call it in anywhere. A for guns, I believe shotguns are legal at all public sites (but check the individual site for possible restrictions on shot size and type), some sights permit rimfire rifles. Check individual sights for details, here:
http://www.dnr.illinois.gov/hunting/...actSheets.aspx
What sights are you thinking of hunting?