First, you need to calculate when the three day notice expires. In calculating that time, day one is the first day after service was complete. If the third day falls on a Saturday, Sunday, or holiday, you have until the end of the next business day to pay your rent or move. After the three day notice expires, the landlord can file the unlawful detainer action. You must then be served with the summons and complaint. If you are personally served, you have five days to respond. If you are served in a manner other then personal service, you may have up to 15 days to respond. Again, day one is the first day after you are served. You do count weekends, but you don't count holidays. If the last day falls on a Saturday, Sunday, or holiday, you have until the next business day to file your response with the court. If you don't file a response, the landlord can take your default. If you do file a response, the court will set a hearing date or trial date, depending on what you file. The trial date has to be within 20 days of when either you or the landlord requests a trial date. If you lose at trial, then the landlord can get a writ of possession and take that writ to the sheriff. The sheriff will then post a notice on the property telling you the date and time by which you have to be out. That date and time is usually 5 days after the sheriff posts the notice. So, even if you do nothing, it is usually at least 2 to 3 weeks from the time you are served with the summons and complaint and the time the sheriff does the lockout.
Remember that eviction cases move very quickly and you should consult an attorney at the earliest opportunity.