The first thing you need to do is issue a 5 day eviction notice. If you Google "5 day eviction form Illinois" you will be able to find the proper form.
Second, deliver the notice. You can either hand deliver it (someone over 13 needs to accept it) or send it certified mail.
Third, complete an affidavit stating that you served the letter. This will be necessary if you have to go to court later.
Fourth, give the tenant 5 days to vacate.
Fifth, if the tenant refuses to vacate, you will have to file a complaint in county court. The county clerk should have the forms you need. When you file the forms in county court, you will be given a summons, which the sheriff will deliver. The summons will have a court date on it.
Sixth, take the summons to the sheriff to serve on your tenant. There is usually a fee for the sheriff's office to do this.
Seventh, show up to court on the date in the summons.
Eighth, if they fail to vacate as ordered by the court, you can have the sheriff forcibly evict them.
You can find more information and forms here: http://www.illinoislegalaid.org/index.cfm?fuseaction=home.dsp_content&contentid=1766#
I hope that answers your question. If not, feel free to ask follow up questions. If so, please remember to "rate" my answer. Good luck!
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