you don't say where you are in northern ohio. I live in cuyahoga falls and our city utility department runs the community garden program. other towns in ther area use their park department or the local men's garden club.
just a hint as to where you can start looking for help.

i stopped participating because our town wasn't willing to do anything to improve the site: they run leaf composting
program but won't spread any on the gardens, moved the site out to wide open spaces with deer abounding-- but won't fence the area, the site isn't ready for planting until after june 12, no storage areas, no hoses allowed, parking is about 1/4 mile away.

I'm in NE Ohio (Lakewood) and ours is run a little differently. Gardeners volunteer for different spots within the city--some of them are small beds within the park, others are those otherwise awkward triangles of land leftover at intersections that are not quite square, etc. Each gardener or team of gardeners take care of their own little area.

If you're thinking of a community veggie garden, I would check to see if your local YMCA might partner up with you... ask around at local nurseries to see if they want to help/give advice... check with your city's utilities department... check with the local school system... maybe also see if your local board of health might have an implementable program...

The Civic Garden Center in Cincinnati runs a community garden; they also offer classes on that. You could contact them and they might have some resources to send. Also could do a google search on "how to start a community garden" and you could probably get some good info.

Good luck!!