I am from Kenya and I'm going to Ohio for a visit. What exactly do I need to have from the airport before my departure?
You'll need a US visa; for a 'visit' (tourism or business) you need one of type B-1/2. If you haven't got one already, this is the website to apply from Kenya.
Once you've got the visa (which is probably the hard bit), the only other difficulty is convincing the border agent that your travel is legitimate and you intend to return home. There's no fixed requirement for any documentation to prove, but things that would help are bank statements (to indicate you've got the money to pay for your trip) and bookings for a flight home.