There are hundreds of companies offering this services, with so many different rates that Germany is often described as a Tarifdschungel (rates jungle). Rates vary considerably and change frequently, so it is almost impossible to keep up to date on the latest developments (for this reason we won't recommend you any provider at our site). You can find current rates under www.teltarif.de.
For many call-by-call providers, you don't even have to register and just dial a special prefix number before the number you want. Before getting connected, you will be told the cost per minute for the call. Charges will then appear on your normal phone bill, so you don't have to make separate payments. However, some providers require you to register with them and sometimes charging a monthly fee and/or asking you to sign an exclusive contract.
If you're calling abroad, you might want to consider buying an international prepaid phone card as these offer the cheapest calling rates available. See our section on calling cards for more information.