You must give them proper notice according to Florida law. If they fail to move by the deadline, then you will need to give them an eviction notice and start eviction proceedings.
If the situation is such that they are violating the lease agreement, you can give them a 7-day notice to cure before evicting them. However, if it is truly month-to-month and there is no stipulation within the lease of a notice period, Florida law allows both tenant and landlord to terminate the agreement with a 15-day notice. Other than that, your lease agreement with the tenant ultimately defines the relationship and your rights.
Carol Johnson Law Firm, P.A. : (727) 647-6645 : firstname.lastname@example.org : Wills, Trusts, Real Property, Probate, Special Needs: Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact me if you feel you need additional assistance with your matter.
I agree with Attorney Johnson. However, because of the complexities and the fact that you may want to pursue the tenants for damages, I recommend that you hire an experienced real estate lawyer in your area to help you with your case.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.