1. Gather data
2. Use family information to delve deeper into family research
Vital records are considered "primary sources" and though the physical artifacts are typically preserved in archives, many have digital counterparts that can be searched online. In Illinois, the Illinois State Archives offers a number of databases to assist in family research. Some Illinois counties such as McLean, have online indexes for records at the county level.
Examples of Vital records
Marriage: Illinois Statewide Marriage Index, 1763-1900
Death: Database of Illinois Death Certificates, 1916-1950 and Social Security Death Index, 1962-2014
3. Ask for help from librarians!