We plan on spending 3-4 weeks in Europe, starting in Amsterdam then Germany and then Prague in the Czech Republic, and returning to Amsterdam to fly back to Canada. Our schedule is open with no specific dates to start or end a country visit, so my concern is... can we buy train tickets at a reasonable price to travel on a last minute whim? Any information including pitfalls that we might encounter would be most welcome.
"...so my concern is... can we buy train tickets at a reasonable price to travel on a last minute whim? Any information including pitfalls that we might encounter would be most welcome." Within Germany, full price tickets at the last minute can be very costly for long distances. On the other hand, the shorter trips you might make within a given Land (our "state", roughly) can be done fairly inexpensively with daypasses for the regional and local trains. Buy them as you go. These are outlined HERE. If you will be making shorter trips across state lines, similar daypasses are available - one version for weekdays, one for weekends; buy them as you go: Quer durchs Land Ticket Weekend Ticket
"can we buy train tickets at a reasonable price to travel on a last minute whim?" Freedom (to travel on a whim) is not free. You will undoubtedly pay full fare to buy tickets on a last minute whim. You can find the price of full fare tickets on the national railroad websites. The German Rail (Bahn) website should show Amsterdam to Germany prices, point-point prices in Germany, and Germany to Prague prices. If you make a stopover in Germany on your way back from Prague, you can find the price for those legs on the German Rail website. Or you can closely estimate the Prague to Amsterdam price by using two legs with a station in Germany. There is also a night train (CNL) from Prague to Amsterdam. For that train it would be highly advisable to book in advance, and with advance booking, you can get reduced "Savings Night" fares. This is a case (last minute, full fare tickets) where you might want to look at a rail pass. A rail pass might (but probably won't) save you money. For German trains (other than the ICE Sprinter), there are no supplements for express trains. Don't think about buying tickets from a US distributor (like RailEurope). Their prices will almost always be higher than the full fare, counter price over there.