I lived/worked in OH in 2018, my wife lived/worked in NY for half of 2018 & then moved to OH and worked half a year in OH. We file jointly for Fed, how do we file state?

It is different for each state.  

For NY, your wife will file a part-year return and may use the filing status as Married Filing Separate.  This way only her income is calculated and taxed in New York. 

For Ohio, you are required to file as Married Filing Joint.  You will input her nonresident period into the Ohio return, and Ohio issues a credit for how much they would tax that portion of income that she earned while living and working in New York.

Thank you very much, that helps a lot. Does Turbo Tax allow for me to file all together or would I need to do a mock MFS Federal return for my wife to submit a New York State return? I know the Federal return typically filters into the State - could you tell me how that works?

If you use her as the primary taxpayer, I know you will not need to use the mock return method (and might not anyways).  That method is usually needed when a married filing separate return is needed for one spouse in one state, and the other spouse needs MFS in the other state.  When you set it up, if the NY return allows her to prepare and file separately on your account, you will be fine because Ohio will be a joint return.  

Great, thank you very much for the thorough response!

You are welcome.