What is the cheapest way to travel around Germany? Are there discount bus lines?

Visit http://www.raileurope.com and research the variety of railpasses available. A German railpass might be just what you need. If you venture outside of Germany, however, there are a variety of Eurailpasses that will serve you well. If you are just doing a few legs, however, it is cheaper to buy point-to-point tickets. You can book in advance online at German Rail’s Web site, http://www.bahn.de, and take advantage of advance booking discounts. generally, travel outside of weekday morning and evening rush hours is least expensive.