Hey guys!
I actually found a neat website that explains quite a few things and also shows how and where to get a free SIM card from one of the major carriers in Germany. See here: http://www.mygermanphone.de/free-sim-cards/

I don't have a German address and they even sent a SIM card to my house in the US for free. Can only recommend them!
They also have a helpful FAQ section: http://www.mygermanphone.de/faq/

Cheers,
Alex