Steel shot is not required for squirrel hunting in Illinois but may be required on some public hunting areas and in all areas where migratory birds are hunted. (See HT Digest 2012 -2013, Hunter Fact Sheet or contact hunting site.)
Either shotgun or rifle can be used.
If you were born before 1980 then you'll need a Resident Hunting License and Habitat Stamp. (See page 8 of the HT Digest 2012 -13) Species: Squirrel (Fox or Gray) Hunting Dates: Aug. 1, 2012 - Feb. 15, 2013 closed Nov. 16 - 18, 2012 and Nov. 29 - Dec. 2, 2012. Hours: 1/2 before sunrise to 1/2 after sunset. Daily Limit: 5 Possession Limit: 10 (a) On the second day of the hunting season, you may only possess no more than twice the daily bag limit.
The Hunting Digest is available at: www.dnr.illinois.gov/hunting/Documents/HuntTrapDigest.pdf