If you are looking for your own flat, the rent is only allowed to cost up to a certain amount. This depends on where you live and the number of people who are going to move in. Find out at the social services department ("Sozialamt") beforehand.
High additional costs in Germany
The rent is made up of several components. The "Kaltmiete" (rent minus additional costs) comes in addition to operating costs (e.g. for waste collection and a caretaker ("Hausmeister")).
You also have to pay a relatively high amount for heating and warm water. The total cost is called the "Warmmiete" and must be transferred to the landlord ("Vermieter") every month. You must always pay extra for electricity, which is directly billed to you by the electricity provider. Note: the "Warmmiete" (rent plus additional costs) is much higher than the "Kaltmiete" (rent minus additional costs).
Flats are usually unfurnished. You must pay for objects that the previous tenant leaves behind. This usually means the kitchen.
When you have found a flat, you must present the tenancy agreement ("Mietvertrag") to the social services department ("Sozialamt"). The Mietvertrag contains all the important information concerning your flat. It applies to you as well as the landlord ("Vermieter"). The Sozialamt will check the agreement. You can only sign it after it has been checked.
Note: You must inform the authorities when you change address!
Tell the Bundesamt (federal office) and your Ausländerbehörde (immigration office) your new address, otherwise you may not receive important letters.