Just as all German citizens do, international students must register their place of residence at the registration of address office / citizens' administrative office.
In Germany, once you have found a flat, a room in student accommodation or a flat share you must register at the registration of address office within one week. This applies every time you move!
You should keep a copy of the registration confirmation with you at all times. This serves as proof of address and you will need it, for example, when you open a bank account or want to become a member of a library.
To register you need your passport or identification card. It also helps to take your tenancy agreement with you to the registration of address office because you have to give details of your landlord.