The 2 week rule
In Germany, everybody, a German or a foreigner, who moves from one city to another city must register themselves at the Resident Registration Office within 2 weeks and notify of their address change. This 2 week rule is generally great but we would strongly recommend to register yourself as soon as possible with the local registration agencies, so that you can move forward with the other procedures for settling yourself in your new home town. After filling out a registration form at the office, you will receive your ‘Meldebescheinigung’ or ‘Meldebestätigung’.
Exception: If you are registered somewhere else in Germany and are staying less than 6 months in another city or if you are from outside of Germany and only planning on living in that particular city for less than 3 months, you don’t need to register yourself at the local Resident Registration Office.
Registration form (which you will generally receive at the office itself).
Valid Passport (non-EU citizens) or ID card (EU/EEA citizens).
Visa, if required, for entry into Germany.
Rental agreement or confirmation letter (if you are living in a hotel/hostel or apartment-hotel type accommodation).
If you have children: Birth certificate (translated in German).
If you are married: Marriage certificates (translated in German).
Things you can do with your residence proof
Although once you have your resident permit with you, you don’t need to take around the ‘Meldebescheinigung’ to register yourself at different places but until you have it, you need to present this document along with your passport every time you want to register yourself somewhere. Some situations/places that will require you to produce a residence proof are:
Opening a Bank account.
Subscribing to a Fitness Club/Gym.
Obtaining a residence permit.
Enrolling at a German university.
Applying for a German tax id number (it's generally required, if you want to start freelancing, so that you can write bills to your customers).
Getting a mobile phone contract.
In this video below, the students talk about how they arrived to Germany and how they went through the process of registering themselves at the local Resident Registration Office: