prague to munch by train

The fastest is bus operated by Deutsche Bahn. There is also a direct train. Train takes about 1 hour longer. You can check schedule on Deutsche Bahn website.

The most efficient way for a family to travel is by train, and there are a number of trains from Prague to Munich in about 5-6 hours. From city to city, flights require travel to the airport, going thru security waiting for the flight to leave and getting into the center city at your destination. Trains usually just go from center city to center city, and are easier to deal with.

Full fare for the bus from Prague to Munich is about 65€/adult, but with sufficient advance purchase, you can get a Savings Fare ticket, for a specific bus with limited refundability, for 29€/person. Assuming 3 adults (15 & older), that's as low as 87€ with advance purchase. For the train, a Czech Rail ticket, purchased for about 10€ (equivalent in Kc) in Prague, will get you from Prague to the German border. You can purchase a Bayern-Ticket online from Bahn.de for 22€ for the first person, 4€ additional persons up to 5 total. That will get you from the border to Munich. The online-purchased Bayern-Ticket will be valid for the day specified on any regional trains in Bavaria. For 3 adults, that's about 60€. You could save a little more by using a Czech Rail ticket only as far as Pilsen and then using a Bayern-Böhmen-Ticket from Pilsen to Munich, but the Bayern-Böhmen-Ticket is only available in Germany or from the German language Bahn Ticket Shop, so if you can't read German, that is probably not an option.