How do you have to go about evicting a renter that hasn't paid rent for 3 months when a lease was not signed?

You follow the same procedure as if there were a lease. You send them a pay or vacate notice with the time required by your state's laws. Then you file a lawsuit for eviction if they don't pay or move out within that time.

At the top of the Real Estate Law forum is a sticky post with links to the laws for all of the states.

Well first you don't let them stay 3 months without paying. Can I assume you are a new landlord, the first thing before you ever rent your first house or apartment a landlord needs to get all the legal forms to evict, know all the laws, where the court is and more.

Have you served them official notice to pay or quit ( pay or move out) if so, you file in houseing court for a formal eviction.