My advice:
1. Read up on Illinois RUT-50 -->
https://www2.illinois.gov/rev/forms/...t-50-instr.pdf
Note that your tax will end up being $15, (see step 4.2)
2. Find a SOS facility that does title and plate transfers.
3. Go into the facility, with your signed over title and ask for RUT-50 (tax) & VSD-190 (title & reg) . You will have to explain what you are doing with them since they are not used to having people coming in prepared and knowing what docs they need.
4. Fill out forms, pay your $15 and you are done. Wait for your new title to come in the mail.