Does anyone know how to evict someone in the state of Illinois?

My mom owns rental property and her renter pays his rent like every 2 months and it is due on the 9th every month! He catches up but is never on time.......can anyone help her because he already told her he can live there for 3 months free before she can actually get him out! Is this true?
Update: they have no lease it is a verbal commitment on the renters part, but he agreed to pay on the 9th of every month! I told her make up a month to month lease agreement but, since it is just verbal can she just tell him to leave or not? She has a prospective renter ready to move in and pay monthly but she cannot get... show more they have no lease it is a verbal commitment on the renters part, but he agreed to pay on the 9th of every month! I told her make up a month to month lease agreement but, since it is just verbal can she just tell him to leave or not? She has a prospective renter ready to move in and pay monthly but she cannot get this guy out of there
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