Landlord Question and Answer Forum

I am in the process of evicting my renters that are month to month and signed the lease agreement thru landlord forms. I gave the renters a vacate letter along with a non-renewal of lease certified mail. The renter said she is not moving out and told me to bring her to court. She has not paid rent for september and owes 7000.00 dollars in back rent along with never paying on time. I wanted to know the steps to take for evicting them as soon as possible with out spending lots of money. Also It getting to be winter here and i am afraid the courts will let them stay in the house and not pay rent, is this possible that the renters will be able to do that since they have kids? Any advice would be great.