You may go download the Standard Form 76A - Registration and Absentee Ballot Request - Federal Post Card Application (FPCA).
Instructions for the Form
Fill the application out completely and sign it. Ohio does not require a witness / notary
The FPCA is good only for the calendar year in which it was mailed
By mailing a new form each January, or if your mailing address changes, it will ensure that a ballot can be sent for each election
If you wish to vote in a partisan primary election, you must include the party ballot that you would like to receive. Ohio allows you to submit the FPCA by mail, email, or fax
Or, you may download an absentee request to have a ballot sent for one election. It must be mailed, as Ohio law does not permit the faxing of ballot requests. Please include an email address, if possible, on either application.
Send your completed request to:
Greene County Board of Elections
551 Ledbetter Road
Xenia, OH 45385