Planning on using train from Berlin to Vienna, stopover at Dresden, and Prague. Any suggestions on purchasing tickets? Online, in advance, or at the train station? Would a ticket allow a few days stopover at different cities en route? Or, should be purchase one section at a time?
If you book well in advance (up to 90 days allowed) at www.bahn.de, you can get a Dauer-Spezial fare of €29 for Berlin-Dresden and a Europa-Spezial fare of €19 for Dresden-Praha. These are non-refundable and non-exchangeable. However, buying tickets at the station isn't a whole lot more expensive for these routes.
If you book well in advance by phoning the Austrian Rail call center, you can get a SparSchiene fare for Praha-Wien. See here. Dial 011 (US international access code) + 43 (country code for Austria) + (0)5-1717. Omit the zero in parentheses. It is only used for calls originating in Austria.
One thing to keep in mind is that if all your stops are on the same direct route, you need only buy one ticket and then get separate reservations for the individual legs. I believe most tickets are valid for at least 2 months so this will save you the hassle of buying multiple tickets. I must say I'm not sure if this saves you a lot of money but may save some of the hassle.