1. The easiest way to get to Garmisch from Munich is by train (Deutsche Bahn):
http://www.deutschebahn.com/en/start/
There is a direct local train from the Main station (München Hbf) to Garmisch-Partenkirchen, that takes about 1 hour 22 minutes.
If you travel from the Munich airport, you can take S-bahn first and make a connection at the main train station (the total trip would be about 2 and a half hours).
You can get a "Regio-Ticket Werdenfels" for 20 euros, which allows one to travel on any train both from the airport and from the Munich main train station to Garmisch (and back).
There are Deutsche Bahn ticket machines and sales desks at the airport as well, i.e., if you travel from the airport, you should buy the ticket at the airport.
NB. You need to write your name on the ticket to make it valid.
If there are several people coming together, then there is a group rate reduction, e.g., 26 euros for two people etc.
The Atlas Posthotel is about 15 mins walking distance from the train station in Garmisch.
2. If you plan to travel around, e.g., to see many beautiful castles or mountains in the area, then renting a car would be a good option. Public transport in that area is rather sparse.
