Hiking can be as simple as taking a walk along a trail through a wooded area in a State Park in Ohio (a good place to start), or you could fly to some exotic location on a multi-week trek over 10,000 foot mountains camping out, and eating wild foods along the way (probably not so good if you're new to this!!).
While you don't absolutely need to have hiking boots, you do want sturdy shoes and heavy socks. If you're using footwear that's relatively new, wear them for a few weeks prior to your first hike. There's nothing like going for miles with a blister on your foot to turn you off to hiking after your first trip.
I'd start with something easy like a trail at whatever state park is closest to you, you should be able to get a park map at the park office, and you can ask for suggestions on what trails to take that aren't too difficult where you could walk for about 1/2 day. This way , you'll have a marked trail to follow, and there should be bridges at stream crossings.
You will want to take some water for drinking, and maybe some snacks, but you don't want to carry too much. What doesn't seem heavy at the beginning of your walk, may by the end of it. If it's a scenic area, you might want to take along a camera. I use a fanny pack that has a big enough zippered pocket to keep my camera and two water bottles on either side. You could also use a backpack if you have one if you wanted to take it along. For 1/2 day, though, it really wouldn't be necessary. If you like birds or flowers, you could take a field guide to identify what you see along the way. A small first aid kit isn't a bad idea, even if it just includes a few bandages and some alcohol-based sanitizer.
Check the weather ahead of time - you don't want to be several miles from your car and buildings and get caught in a thunderstorm. If it's cool at the beginning of the day, wear several lightweight layers you can take off as the day warms up. Or if it's warm when you start, have a light jacket if you'll be out toward evening and it might get cooler.
Have a hat (it not only keeps sun off, but annoying bugs) and sunscreen. Even though there might be trees overhead, if you're out long enough, you can get sun from the openings between the trees. And bug spray, at least to keep in your car to put on before you go out. You can do the same for the sunscreen.
Don't try to do too much too soon. Take an easy trail or a moderate difficulty one, don't head for the top of the mountain or bottom of a gorge your first time out. If you get tired, take a break. And it's a good idea to have a second person along, or at least make sure someone knows where you are, what trails you'll be using, and when to expect you back. Accidents can happen!!
If you start small and local, you can build up to day-long hikes, then backpacking with camping. You might see if the local state parks or an outdoors store has day classes on hiking, map reading, using a compass, and camping. There used to be one store in my area where the store employees had weekend day classes and overnight trips, so you could do this with someone experienced and be in a group of people. Or, you could join a guided walk at the park (these usually run 1-2 hours, and your guide will talk about the wildlife or history of the area). The more you know about being outdoors, the more comfortable you'll be.
If you want to look for boots, look for soles with deep lugs for gripping, and that are at least a little stiff and come up over your ankles for support. But overall, look for something that feels comfortable on your feet. Wear the sort of heavy socks you'd be wearing outdoors when you try boots on. From standing flat, raise up on your toes, and bend your ankles at different angle to see how they feel. I usually have 2 pairs, one with mesh sides for summer hiking because they're cooler, and one heavier, insulated, waterproof pair for winter, wet locations, and more difficult terrain. But you won't need these your first few times out.
Some websites with hiking tips: http://hiking.lifetips.com/cat/62953/hiking/index.html
http://www.hikingdude.com/hiking-training.shtml
http://www.hikingwebsite.com/hiking/howto.htm
http://www.closertonature.com/outdoors/hiking-backpacking-tips.htm - all levels
http://www.thebackpacker.com/ - a little more advanced, but it has gear reviews if you ever want to buy equipment
And on hiking in Ohio State Parks: http://www.dnr.state.oh.us/facilitiesmaps/ohiohiking/tabid/502/Default.aspx
http://www.stateparks.com/oh.html
Have fun!!
