Yea the turtle loves water and feels more comfortable in it. You should set up at least a 55g but that turtle is already about too big for that so definitely bigger is better. Also don't forget a basking area to get out of the water and warm up.
Water turtles live in water. They only come out to sun themselves, lay eggs or move to another location. They can't swallow their food unless they are in the water. This turtle is big enough it needs to live in an outdoor pond.
Please check Ohio's regulations about taking native wildlife from the wild. It may be against the law to have picked it up.
I suggest the same as Lexiii. It is often times difficult for a wild turtle to adapt to captivity and they could die from the stress of trying to escape/refusing to eat. Doesn't happen all the time, but it happens enough that I felt the need to give that warning. There are many sliders looking for new homes on Craigslist and PetFinder.com all the time, any of them would be a good match given the proper enclosure. But yes, most slider species, especially the females, will need an outdoor pond because of the minimum enclosure size requirements. Painteds, muds, and musks can be kept inside all their life as they tend to stay small. A Razorback Musk can be kept in a 40 gallon aquarium, though bigger is always better.
Incidentally, in water turtles, both males and females have a smooth plastron (bottom shell). The way to tell the difference is by the size of the tail, and where on the tail the vent is. Males have big tails and the vent (cloaca) is far away from the body.
Wait a second. That's a yellow bellied slider, a Trachemys scripta scripta. If you live in Ohio, I would venture to guess that this fella isn't a native. Last I remember, T. s. scripta didn't occur north of Maryland or east of the Appalachians. You can tell it's a yellowbelly by the yellow S behind the eye, which is distinctive to that particular subspecies. What you have could very well be a released or lost pet.
Try feeding it some commercial pellets, Mazuri Koi food or turtle chow. An animal that size could also consume various leafy greens as well as crickets, roaches (any moving insect that isn't poisonous, really).
Set the turtle up in a large water bin (stock tanks from an agricultural supply store will work, as will a large cement mixing tub from a hardware store, though a large aquarium around 55 gallons will work temporarily; as with all things, the bigger the better, with 200 gallons being closer to a permanent minimum). Whatever you do, do not release this animal back into the wild. As I said, yellow bellies are not native to Ohio, especially northeast Ohio. From what I remember, painted turtles and snapping turtles are the only species native that far north.
Also, check the regulations. If I remember correctly, Ohio has some rather draconian nanny state regs regarding the keeping of turtles and tortoises. Once you research the exact nature of Ohio state law regarding the keeping of turtles, you can research on the forum a more permanent solution for your new little lady, or contact the proper authorities.