Most German prepaid SIM cards generally suck with tiny 200mb 3G data allowances, don't even bother looking for prepaid LTE/4G...
The best by far seems to be C
ongstar, it's all in German, including text images, so Google Chrome translating isn't always helpful, so you will need to have a smattering of German to work it out and register.
You can by a prepaid SIM card from
DM for
€8.49 which includes €10 credit, or from any
http://www.telekom.de shop, lookout for the pink T sign, for €9.95.
(BTW Congstar uses the t-mobile network, supposedly the best in Germany, but they only sell the SIM packs, no in store support)
There are two SIM packs, one in plastic which lets you choose options, the other one has a choice of two plans.
If you are like me, only after data, you can get 1Gb for €12:90 for 30 days which I think is the best you will find. 3Gb is only €19.90
Viel spass!
UPDATE
1. You can find out how much data you have used via
pass.telekom.de, (not via WiFI or WLAN as the Germans call it)
2. This is annoying, surf packet (data) is per month, so once you have used up your data, you are speed limited to 64k. You can't upgrade to a higher plan until the next month, which is really dumb. You can however, via
speed on, purchase a 500mb upgrade, via the
pass.telekom.de, so I would really recommend the 3GB option
3. The live chat support via
congstar.de is quite good and if you ask them to speak English they can :)