i''m on a month to month lease when i turn in notice to move am i still responsible for that months rent?

When a tenant is on a month-to-month lease term, the tenant must give at least 30 days written notice of his or her intention to vacate the premises.  The 30 days begins to run from the date that rent is due, usually the first day of the month.  For example, if the tenant gives 30 days notice on the 10th of the month, the tenant is responsible for that month's rent and the next month's rent -- because the tenant's 30-day notice to vacate does not begin until the 1st of the next month.  It is crucial to pay attention to all notice requirements contained in the lease (if there is a written lease).