Although Lufthansa and other airlines have a great network of flights within the country, on the whole the best way of getting around Germany is to use the Inter-City- Express (ICE) trains, that operate between almost all of the major cities and are very good value as well as being almost as fast as flying. A comprehensive local train service that will almost certainly serve any city or town you care to mention supplements these.
In the cities, the buses, trams and underground services will get you around with ruthless efficiency, while taxis operate door to door, and are usually in the form of a comfortable Mercedes of BMW.
Hiring a car is a tempting option in Germany, and the Autobahn are high quality roads on the main routes that have the (dis)advantage of not having speed limits on all sectors. On the unlimited sections, you should tend towards driving fairly defensively, as it is not unusual to see other Porsche drivers making attempts on the land speed record in the outside lane.