If you are from continental Europe or your flight goes to another city than Hamburg you might want to use the train.
These are mostly operated by the de facto monopolist Deutsche Bahn and tend to be rather expensive.
However, if you book earlier - not earlier than 90 days though - you have the chance to get to purchase a reduced ticket ("Sparpreis")!
Generally, it is a fast and pleasant way to travel.
For further information, visit:
In Germany, it is quite cheap to travel from one city to another by bus. This is certainly not the quickest way to travel but if you need to travel inside of Germany and you want to save some money, its certainly a cosiderable option. One of the most useful comparison/search sites can be found here: