As you may have noticed from my post on Frankfurt’s free airport wifi, free wireless internet in German airports and Germany in general, is hard to come by.
You can get on the internet at Munich Airport (MUC) in Terminal 2 at a kiosk of four computers offering free internet. These have German keyboards so a few keys may give you pause. (The Z and the Y are swapped, and to get the @ sign you need to do Alt-Gr + Q)
To get to these computers, pass through security, turn left toward Gates G 1-17, and you will see it on your right as you come to the first moving walkways.
Telekom offers 30 minutes of free WiFi. When you connect, the login page comes up and you need to enter a cell phone number to receive the pin number. I entered mine but never got it. I was using a Thai cell number, so that may have had something to do with it (though I had received text messages before using it in the airport and the options for Thailand and many others are listed in the menu of country codes for pin section.
Outside the security area there is a Starbucks in Terminal 2. This is worth a try as well, but be sure to give yourself plenty of time to get back through security for your flight; I found security a bit slow and Germans didn’t seem to be in a big rush.