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.
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.