First you pay taxes to City/Municipality where you work. Then you pay taxes to the city where you live, if require. Most Municipalities where you live will give you credit for the taxes you pay to the work city. An Example: Live in Columbus (2% tax), work in Westerville (1.25% tax). Paid 1.25% to Westerville and then .75% to Columbus, total 2.0%.
Link to all Municipalities forms.
http://tax.ohio.gov/divisions/municipalities/index.stm