Hi,

the train is an option, if you can get a cheaper promotional ticket, but usually it is quite expensive.

You can try for a flight, sometime Lufthansa offers flights starting from 99 Euro on a return flight. Check at their website.
www.lufthansa.com

Another possibility is the "Mitfahrzentrale" , this is some official way of hitchhiking. Drivers offer available seats in their car and charge you part of the gasoline costs.
As this is done over a profit organisation, they charge you a small amount on top, but then you are insured and it is safe, because drivers have to leave adress, show their passport, etc.
You can find more information here:
www.mitfahrzentrale.de
I used to do this when I was a student, but you never know how the "driving style" of your driver will be and it can be daunting sometimes.

Probably the best and cheapest option for you is the bus, called "Europabus". They part from the busstation in Froettmaning (where the Allianz Arena is) and the price should be well under 40 Euro (I don't know the exact price).
http://www.inside-munich.com