By bus and train
Offenburg is easily reached by train from Basel, Baden-Baden, Karlsruhe on the north-south axis. Some ICE trains stop here as well as the local trains. Other than that here starts a regional train line to Strassbourg (France).
The train station has a few lockers and public toilets (50 cent coin needed). There are lifts to the platforms.
In front of the train station you will find a bus station (picture no. 2). Here you will find local buses as well as regional DB buses.
Rent a bike
Offenburg has the system of "next bike". Since 2010 they have 85 bikes in 13 bike stations. I noticed such a bike station near the Dreifaltigkeitskirche and thought that I must let you and Nemorino know about this opportunity to rent a bike.
You need to register online with nextbike using your credit card and then you can use the bikes in all the countries that participate. Prices from 1 Euro per hour and from 8 Euro per 24 hours.