What, how, where, is the process to evict somebody in Chicago, IL?

Hey Yahoo users: As a recent homeowner Chicago, IL, I recently bought a house for purposes of renting it to other people. The house is a two flat, and I'm currently renting the two floors. Our first floor tenants are great, always pay on time and are very responsible. The problem is with my second floor tenants. She is a young mother of two small boys (the contract was for three people) although now her "husband" who she said are separated is now living in the house. That's not the only problem, she ALWAYS pays the rent very late, she acts in a very innocent girly matter and always has an excuse. Her most common excuse is that her husband hasn't been paid yet (although the husband isn't on the lease). I've been very nice and patient with her, last time I gave her a 5 day warning to pay the rent on time or face legal action, she paid me on the second day after the warning, but again she is giving me excuses that she will come me back on a certain time and date to give me the rent, of course she never calls and keeps her promises. Now after all my history with these people, I want to know how can I evict them? Where should I go? How much does it cost to evict someone? and How long will it take approximately? We are in Chicago, IL. in the city. I also want to know if I can begin the process of eviction without telling her when I go downtown (where I suppose is the place to go to evict someone)? Obviously I will tell her I'm evicting her after the I start the process. But again I want to know it I can begin to do the paperwork before I tell her. Thank you.

Sincerely,

A desperate landlord.