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You have to take a train from Munich to Garmisch-Partenkirchen, and from there the rack railway to the Zugspitze. The journey takes almost three hours and the trains from Munich to Garmisch run hourly. Thus it is possible to do a round trip from Munich in one day.
Here are some recommended schedules:
The round trip from Munich to the Zugspitze costs 59 EUR with a so-called "Garmischer Sommer-Ticket".
For more information on schedules you can have a look at the website of the German Railways. Informations about cable cars and alike can be found on the official website of the Bavarian Zugspitz Mountain Railways.