The first point needing clarification here is that the expiration of any notice you issue simply gives you the right to file an eviction lawsuit against the tenant if they have not already left the property. The expiration of the notice alone does not give you the right to evict. You must file suit!
If he has not paid rent under a month to month arrangement, you can issue a 5-day notice for nonpayment of rent. However, when you file the suit and go to court you will be required to prove the existence of this agreement, which likely falls outside of the statute of frauds (this means such an agreement must be in writing in most cases).
Your best course of action in this case is to issue a 30 day notice of lease termination to your tenant. The 30-day notice allows you to terminate a month to month agreement for any reason, not just for a breach. When it expires, you will have a solid eviction lawsuit to pursue if the tenant has not already vacated.
The city and state statutes have very specific notice provisions, so this is best handled by an attorney.
This answer is intended as informational only, and does not constitute legal advice or form an attorney-client relationship between us.
Because the issue is the failure to pay rent, a five-day notice is sufficient. The notice does not need to be notarized or served by a special process server. However, so that you have a record of when it was sent and received, it may be best to send one copy via regular mail and one copy via certified mail with a return-receipt requested.
Reading up on forcible entry and detainer is not sufficient if you do not understand it and/or do not know what you are doing. You would be well advised to hire an experienced eviction attorney. If you attempt to do this on your own and do it wrong, you will have wasted a great deal of time and money. Do yourself a favor and hire a lawyer.