Take the suburban train (S-Bahn) line S8 from the airport to the city. You can purchase a one-way-ticket ("Einzelfahrkarte 4 Zonen") at the vending machine for 11,60 €. Get off at “Marienplatz” station and take the subway lines U3 (direction: Moosach) or U6 (direction: Garching-Forschungszentrum) and get off at the second station which is “Universität”.
How to get to the University from the main train station ("Hauptbahnhof")
Take the S-Bahn (any of the the lines, S1 to S8; direction “Ostbahnhof”) and get off at “Marienplatz” (second station). Then take the U3 (direction: Moosach) or U6 (direction: Garching-Forschungszentrum) and get off at “Universität”.
There are several reliable taxi companies in Munich, e.g.: