Your lease may be up, but that just means that unless you and your landlord make another agreement, you will be on a month to month tenancy, or a tenacy at will. When you are in this situation, either of you must give the other 30 days notice to vacate. But that diesn't mean 30 calendar days. It means that you must notify the landlord before the end of the month that the next full month will be your last. So if you want out ASAP, notify your landloard now (October 8) that you are giving 30 days notice. You will then stay through October, AND November, and may leave by November 30 - If you stay until December 1, you will owe for that month, and may have to start the 30 day clock ticking all over! (BTW, you don't have to physically stay there, but you will be responsible for rent and any other expenses (fuel, electricity, cable, etc) that you previously agreed to cover while a tenant for the duration of the rest of your "time".
Do not forget to do your walk-through, take photos, and have your landlord sign off that you are leaving the property in acceptable condition!