Cook County isn't the best for landlords. (All my properties are in Cook County) The process usually goes something like this (not legal advice)
1. Serve 5 day notice
2. If the tenant hasn't paid by day 5 (you can count weekends but day 5 has to be a weekday), then you can file for Joint Action, which is for possession and rent money. You are assigned a court date about 2-3 weeks from date of filing.
3. In Cook County, it is required that the sheriff serve the summons first. In my experience, they are successful about 66% of the time. If the sheriff cannot serve them, then on the first court date you ask the judge for an alias summons to have a process server give the summons.
4. On the court date, if the tenant had been served, then the judge will hear the case. If the tenant does not showup, then you get a default judgment. If the tenant shows up and presents no defense, then the judge usually gives them 2 weeks to stay and you get a money judgment. The court would prefer if you came into an agreement with a tenant before stepping in front of the judge.
5. If the tenant stays beyond the date stated in the order of possession, then the order must be filed with the sheriff. Now this is where Cook County fails the landlord. In good weather, it will take another 20-30 days for the sheriff to comeout. Currently, it is about 10-12 weeks since they basically did no evictions in Jan and part of Feb because of the cold.
Of course, tenants can bring up defenses and other motions, which would further delay the process.
Cook County landlords: Tenant screening is very important.