After having registered with the Bürgeramt directly after your arrival you will sooner or later receive a letter from an organization called GEZ (Gebühreneinzugszentrale).
The GEZ is the state-run organisation that demands fees for radio and television under public law. Everybody who owns a radio and/or TV set has to pay these fees (the amount of which depends on whether you own only radio or both radio and TV).
In Germany, there are many different radio and TV stations. Some of them are run by commercial companies, they're called private stations; others (e.g. ARD, ZDF, Deutschlandradio, and the regional station SR) are under public law. The private stations obtain their financial means from the masses of commercials they flood us with (and, correspondingly, usually broadcast rather low-level programs in order to force up viewing figures), whereas the public stations are financed by the state and through the GEZ fees. They broadcast fewer commercials (none after 8pm) and try to keep a higher standard of programming.
Now when you get that letter from the GEZ you will find enclosed a form in which they ask you to state the number of radios or TV sets used in your household. If you have got none - and be honest here, they sometimes come and check it - just send the form back with that information, and that's it.
If you do have either TV or radio, you are usually asked to transfer the fees to a certain account using a direct-debit mandate. A special form for this purpose should be enclosed in the same envelope; or else you will receive that later. If you don't approve of this method, you can also transfer the money in single units every month (either one at a time or by standing order).