You must be a resident of the state of Ohio for 45 days, and a resident of the county for 30 days.
You can apply in your county OR in an immediately neighboring county.
You'll want to read the official 2011 Concealed Carry Laws Manual. It spells out everything you need for applying.
Here is the place to download the manual and application: http://www.ohioattorneygeneral.gov/ConcealedCarry.aspx
Hope you enjoy Ohio!