If you plan a longer trip to Germany you will want to be reachable by cell phone and also be able to call people in the country at a reasonable rate. Public telephones still exist (although they seem to diminish), but these too often can only be operated with telephone cards - sometimes with cash, but paying a little more you avoid the hassle of searching for one of those booths.
There are telephone shops in the center in most shopping malls. You just have to bring your passport along for the registration and in a couple of minutes you have your German sim card. There are several large companies like Vodafone, Telekom, 02, Debitel offering different rates for telephone and mobile internet access.
Follow this link on Google Maps for a list of the shops downtown Stuttgart.
By the way - don't be surprised, in German a cell phone is called "Handy".
Most shop assistants hopefully will also speak some English. The rates are changing constantly and are becoming always more complicated, you might want to inform yourself first online before getting a telephone card, however getting a prepaid card doesn't imply any bad surprises and you can always get another one if you are not content. Uploads for the cards can be bought in any "Kiosk" - a small shop which usually sells newspapers, cigarettes and travel supply - you will find them at almost any train station, the airport or also at the gas stations. There are also a couple of vending machines selling the uploads. The uploads are small cards with a hidden code, you have to scratch the cover of the code with a coin - alternatively you will get a small piece of paper with the code printed on it.
Other companies offer uploads on the internet - either manually or regularly, you can pay by credit card, paypal or by deduction from your bank account. I can recommend discotel at the moment. They offer low rates for phone calls and a monthly rate for mobile internet access.