1. Look on the TARC website, www.ridetarc.com
to find out what route(s) you need to get where you're going. There is Trip Planner that will help, and you can look at maps that lay out the routes.
2. Once you know the route and where it stops, plan to get to the stop about 5 minutes before the schedule says the bus is due to arrive. TARC buses aren't early all that often in my experience, but it does happen and you don't want to miss yours.
3. If the driver sees you standing at the bus stop, the bus will stop for you. No need to wave or signal or anything.
4. When you get on, you can pay cash for your fare or use a pass if you have one. You can get monthly passes (check the TARC site for details) or you can also buy strips of discounted tickets at places like Fifth Third Bank branches.
5. If you're paying cash, you need exact change. It's $1.50, and the fare machine takes coins or $1 bills. If you're using the strip tickets, you feed them into the bill slot faceup. If you have a monthly pass, just show it to the driver as you board.
6. If you need to transfer to another route, take a paper transfer slip from the driver when you pay your fare. It'll be good for two or three hours, and you just show it to the driver of the next bus you board.
7. Find a seat, and pull the yellow rope when yours is the next stop. Make sure to pull it at least a few seconds ahead of time so the driver has time to stop at the right place.
I think that's all you need to know.
(And, now that I typed all that out, I find I could have just directed you here: TARC: How to Ride TARC