Notify the town hall of your arrival
After moving into a German town, you have one week to register at the town hall or residency office (Bürgeramt).
Update: Jan 2014
There, you will receive a confirmation of your registration (Anmeldebestätigung). In order to go through this free but obligatory procedure, you need the following documents: a completed registration form (Anmeldeformular), a valid identity card or passport and your rental agreement Mietvertrag) or sales contract as proof of accommodation. If you move again within Germany, you must notify the authorities of your change of address (abmelden) before leaving and re-register in your new town.