It probably goes without saying that the public transportation system is wonderful compared to the US.
Pricing: Base pricing depends on distance - 4 or fewer stops, all around Bonn, the Bonn-Koln region, etc.
Per trip prices are just under 3€ for the all around Bonn ticket (you are allowed to transfer, but not, stop and get back on).
Then there are the day passes. If you are making more than 4 stops (to work, to the dry cleaner, to dinner and home for example) - it’s cheaper to buy a day pass. They allow you to ride as much as you like.
Best part of the day pass - you can get one that is valid for up to five people. It costs less than 5 one way tickets (under 13€), so if you and someone else are making a couple trips, it’s very worth it. Perfect for a family outing or tourists. Everyone has to be traveling together, but has been fabulous for us several times.
Weirdest part as an American - it’s mostly on the honor system. You get on the bus or tram and maybe someone will check to see if you have a valid ticket. This doesn’t happen often on the local transport (Daniel’s only had it happen once, so has Meg - over the last year with almost daily travel). The fine for not having one is pretty hefty (I think it’s 50€ for a first offense).
Another cool part: Going into a train station at 7:30 on a weekday and seeing hoards of kids (7-18) traveling to school with no parents trailing after them.
Seeing kids without adults on the buses and trains is very common. The other week, I was waiting at the bus stop with 4 kids - maybe 3rd grade. As the bus pulled up, one left (presumably to go home after hanging out with her friends) and the other three got on. They got off at the big city park a few miles up the road.