The train ("BOB") will take you from Munich central station to Tegernsee station in an hour. There are multiple coaches leaving from Munich central station, be sure to enter the one that says "Tegernsee".
Public buses are driving around the lake from early morning until about 11 PM.
Most hotels provide free tickets for public transport ("Gästekarte"). Just ask at the reception.
Bus numbers and frequency differ wildly during the day. Because of this you should plan your trip on bahn.de. Here are the names of some important bus stations: