In the state of Ohio how do I evict a non paying person

First you have to send them a written notice by certified mail, return receipt requested, by handing it to them personally or by leaving it at the premises. The notice must give them 3 days to pay all amounts due or vacate the property. The notice must contain specific language that you can find at Lawriter - ORC - 1923.04 Notice - service. (http://codes.ohio.gov/orc/1923.04) in the second paragraph of section (A).

If they haven't paid in full or vacated the premises after the 3 days are up then you can file a lawsuit for eviction.