Political Participation refers to activities that attempt to change society by direct engagement with the formal structures of the political system: voting, running for public office, acting on behalf of a candidate, writing to or otherwise lobbying an elected official in an attempt to sway their opinion or gain their vote, etc.
At the University of Chicago, the Institute of Politics offers a dizzying array of opportunities to study and engage in all aspects of the political process. Follow their website and their various social media channels for events, guest speakers, seminars, civic engagement projects, get-out-the-vote efforts, volunteer opportunities and internships with political campaigns and government offices, and post-graduate public/government service.
Off-campus, many students get to know Chicago politics by volunteering or interning with the office of their local Alderman (i.e., the Chicago City Council representative for a region of the city). The City of Chicago website maintains a listing of all ward offices and boundaries here. Similar opportunities exist within the offices of the State of Illinois' General Assembly members -- to find the representatives and senators for a particular ZIP code, click here.
Consult the Institute of Politics website for information on seeking volunteer positions or internships with US Representatives and Senators from the State of Illinois or your home state. The Office of Civic Engagement also maintains offices that formally interface with State and Federal government bodies for the purpose of influencing policy and legislation.