You do not have to move until the landlord serves you first with the proper notice.   If you have been living in the apartment for less than a year, the landlord must give you a 30 day notice. If you've been living in the apartment for at least a year, but not more than 2 years, your landlord has to give you a 60 day notice. And if you’ve been living in the apartment for 2 years or more, your landlord has to give you a 90 day notice.   After the time on the notice expires, the landlord may then start the eviction process in court. And if the landlord is successful in getting a warrant of eviction, the sheriff will come and physically remove you if necessary. But you will not be forced to leave until that entire process is complete.