I sent a 30 day notice to my tenant that we are not renewing the lease. What happens if they do not move out on the last day of the lease? Do I have to take them to court and have them evicted?

Yes.

You will probably have to give them written notice or right to cure, once that expires, you will have to proceed with the eviction process.

Some jurisdictions allow the landlord to process and eviction, some require it be done by an attorney, you need to check with your local court house to verify the proper procedures.

If they have not vacated by the deadline, the next day you should be in housing court filing for an eviction order.