Each subsequent change of address must also be registered with the relevant local authority. This rule applies to everyone, including German nationals.
To register you need to present your passport and visa (if you have one), a copy of the lease or rental agreement and a completed registration form, which is usually available at the Einwohnermeldeamt. Offices and agencies have varying opening times, particularly in the afternoons, so check before you go.
If there are no problems, you will be given a confirmation form (Anmeldebestätigung) as proof of your registration. Make a copy (or several) of the Anmeldebestätigung as you will need it a lot during your first weeks in Germany. This serves as a proof of your address and a lot of institutions like banks, libraries etc. will ask for it.
At the Einwohnermeldeamt, you will also receive an income-tax card, if you're eligible for one. Give this to your employer, who will use it in deducting income and social security taxes.
You need your residence registration first in order to apply for a residency permit. Once you have obtained the Anmeldebestätigung, take it to the immigration office to get your residency permit. For more information click here.