I have tenants whose lease is up and have not paid two months on the rent and I have notified them that they need to vacate the property by the end of last months and they said they won't move and are still in the house. How do I do a 3 day eviction in NY state without paying a lawyer?

You don't need a lawyer but if they do not leave in the 3 days you will need to pay the small claims court for an eviction by them. Then after that 3 days the sheriffs will remove them.

You send them or hand them a written notice that they have 3 days to move.
NYC Housing Court (http://www.courts.state.ny.us/courts/nyc/housing/eviction.shtml)