The best way to quickly find info on divorce in your area is to Google "Divorce Ohio". I did and this was one of the sites that came up: http://www.divorcenet.com/states/ohio/ohfaq02
It gives general info and helps you decide the best action to take.
Also findlaw.com is a great resource to find information on any kind of law, including divorce. Here is a link to divorce attorneys in Ohio http://lawyers.findlaw.com/lawyer/practicestate/Divorce/Ohio.
I suggest that you take any and all evidence you have (of his cheating), make copies of it and secure it. My husband's family found out that I was saving evidence of his infidelity and while I was at work they came into the home and stole it and shredded it! Not trying to scare you but it is good to make sure you have everything secure. Good luck.

Cheating means nothing in the era of no-fault divorce. Some states may allow infidelity to disallow spousal support, but it means nothing in custody or the division of assets.