From Munich take any train that goes to Garmisch-Partenkirchen (2h). There should be one every hour.
Then a Bus (30 min) to Eibsee. This one too pass by every hour. Exit the station and take a left, after 20 meters cross the road and you are at the right bus stop.
If you are a group, use the Bayern Ticket to save money. It’s valid from 9 am.
Food is bad at Eibsee, grab some sandwiches before, to eat in the nature.
The ring around the lake is 7 km long.
The are several little islands reachable by swimming, or by boat/pedalos.
Check the local weather, it vary so much from Munich, generally more chilled.
WORD OF THE DAY (de): Wandern (Hiking)