Registering your residence
As soon as you have a new apartment and thus a new address, you are obligated to register with the registration office. To do this, go to your local town hall (Stadt-, Verbandsgemeinde- or Verbandsfreie Gemeindeverwaltung) of the area you have moved to. If you register too late, you may have to pay a fine. Under the following link you will find the exact address of the authority responsible for you.
In Germany, an obligatory fee must be paid to finance the public broadcasters of radio and television. The so-calld "Rundfunkbeitrag" is to be paid by every registered household. Changes of residence must be reported to the "Beitragsservice ARD, ZDF und Deutschlandradio". Find out more on their website.
You can find out what else you should do after moving on "Make it in Germany" portal.