What is the process for terminating a tenancy in NYC by a landlord.

Could you give us some more specifics on your situation? I don't know what you mean when you say "by a landlord." Are you a landlord who is asking how to terminate your tenant's lease? Or are you a tenant who is asking how a landlord should legally terminate the lease?

How long have you/the tenant been living at the premises? What is the reason for terminating tenancy? Is there a written lease?

It depends on WHY the tenancy is being terminated. Why would you think that was not pertinent information?

Please provide enough info so we can give you correct advice.

I am the landlord. I have a three family brownstone and rent one of the units. There is no lease, and I want to terminate the tenancy. I also live at the residence. The tenant has become an irritant and I want them out.

Ok, then the tenant is a month to month tenant. Deliver a letter to them stating:

Please be informed that I am terminating your tenancy as of 11/30. Please vacate the premises by that date. Let me know when you will be moving as soon as possible so we can schedule a walk through.

You need to give them one full rental period notice. That's why the 11/30 date. If you had responded to the follow-up questions after you first posted you might have been able to get them out by 10/31.

If they do not leave by 11/30, then on 12/1 you need to go to the local Housing court and file for an eviction order.