@Carey Branam . Typically your lease will have a Paragraph about what Notification is required on how the lease is terminated at the end of lease.
For example, the Texas Association Of REALTORS (TAR) Lease says (Paraphrase) the lease will extend and continue on a Month-To-Month basis unless either party gives the other party Notice Of Intent to Terminate the Lease in accordance with the previously agreed period of notice. This might be a 30-Day Notice Of Intent or whatever period of time was agreed to in the lease.
In my example, if you wanted Tenants out at end of August, you would have needed to provide notice prior to end of July.
You give the tenants a notice of non-renewal either 30, 60, or 90 days prior to the end of the lease (depends on your local rules). Now, that's just a notice of non-renewal. That's not a guarantee that they will actually move. What I would do is, about 15 days before their expected move out date, schedule a pre-inspection of the property. That way you can look for signs of packing which will indicate that they are preparing to move.
I caution against signing a new lease for the day after the old tenant is expected to be out. Many "investors" are greedy and want to turn the property over in one day. But depending on your tenant type this can cause problems. What if you sign a lease for Sep 1 but the old tenant decides they don't want to be out by Aug 30? Now you have a REAL problem! And yes, it does happen!
As stated, you give notice of non-renewal which must comply with your lease AND your local laws. One point to add, is some states stipulate that you must have a reason to non-renew, and cannot just "kick them out." Make sure you are in compliance with all local laws.