By public transportation (S-Bahn) to Herrsching; from there an approximately 3km hike through beautiful scenery, or take a bus or cab. Taking the car is not advisable, at least not if you plan on driving (see Drink, below).
Kloster Andechs is about 30km southwest of Munich, pictoresquely located on a hill between the Ammersee and the Starnbergersee. It is surrounded by grazing grounds for dairy cattle, and the Alps sit off to the horizon in the South. Take a seat, and just look around. No matter the time of year, the scenery is beautiful.
It is fair to say that most "pilgrims" these days come for a spirited experience, rather than a spiritual one. Bavaria is full of baroque churches, but Andechs is famous for its outstanding brewery. The monks of Andechs have been brewing beer for more than a thousand years. They have indeed perfected the art: among the locals the beer is rated as one of the best in all of Bavaria, thus possibly in the world. In the monastery's Schankstube (think pub, not restaurant) it is drawn directly from huge, oaken barrels and is just incomparibly smoother than the carbon-pressurized stuff you might normally be served, and incomparably fresher than what you could get out of an exported bottle. Beer neither stores well nor transports well. If you like beer at all, here you can taste it at the source, and what a difference!. Enjoy either the light or the dark beer; tasting both might be a challenge since it is served in the traditional well-filled 1 Liter steins and the Spezial (special) or Doppelbock (double buck goat) are quite strong. The pretzels are the large kind that is typical of Bavarian beer-gardens, big as a plate, with a thin crust and a soft, bready interior, perfect with a large, white, thin-sliced radish, generously sprinkled with coarse salt. This would be your afternoon snack - outside, in the sun, or under the arched ceiling inside, this place breathes the spirit of old Bavaria like few other (and certainly few of those that are frequented by foreigners). Prost, Herr Nachbar !