Appeals are not accepted prior to assessment notices being sent out. At that point you have 30 days from date of publication to file a complaint. Typical publication is early August.

1) The Winnebago County Supervisor of Assessments: The cheat sheet for The Illinois system for appealing property assessments (Abridged Version)
2) The Winnebago County Board of Review: Official Rules and Procedures (Unabridged Version)