There are several ways to do research on campus. One way is to discuss your interest to do research with your faculty advisor and/or your chief advisor in your department. They will normally be able to steer you towards specific opportunities and/or faculty conducting research in your area of interest.
You may discuss your interest with faculty in your major as well. You might view their research websites to know what areas they do work in.
There are a couple of formal opportunities that we have on campus. MEP students should apply through ISUR. These are described in the engineering wiki:
http://wiki.engr.illinois.edu/display/ugadvise/Research+Opportunities
Also, the National Science Foundation (NSF) sponsors research at different campuses, details at: http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=10006.
College of Engineering wiki:
http://wiki.engr.illinois.edu/display/ugadvise/Research+Opportunities
National Science Foundation (NSF) website: http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=10006.