The best-known telephone operators in Germany are Telekom (T-Mobile) and Vodafone. The easiest way to get a prepaid number is to look for one of these carriers (hint: there are thousands of stores spread out in the city) or buy a chip directly from Saturn (or similar store). You can also try visiting your local Lidl, Penny or Aldi and check out their networks (they usually provide really good value for the cost). The value of the sim card + activation + opening balance is usually something between € 10 and € 25.
Often you will be required to show your passport when activating the simcards. Although some of them can still be activated with out one.
You can also buy a simcard from Lebara from the electronics store at the airport (Tegel). Lebara is slightly more expensive than Vodafone and Telekom but you can buy it at the airport. It also has a great iOS/Android application which is in english.