Any official documents you need, you get from the Bürgeramt (administrative office for citizens). Now the Bürgeramt deals with basically all administration issues you need to be done not only registering your new residence or applying your new passport, but also income tax issues, children allowance related issues, change of driving license and other issues I don't even know. Previously there have been different offices for different purposes.
When you're residing in Berlin, you'll have to register at the Bürgeramt same goes if you change your address. You can go to any Amt not only the office in your district.
Apparently administration was supposed to become more customer friendly by combining different departments but in reality the employees simply have too much work to do. The working staff is overwhelmed and not enough to deal with the amount of work and this for us, the customers, means LONG waiting hours. You can make an appointment booking by internet but it will be at least 4 weeks before a available date. If you can wait - good for you. However, for pressing issues, visit the Bürgeramt during their opening times and make sure you don't have other commitments on that day. Anyhow, check their website before visiting. Also you can download all the necessary forms beforehand and fill them out peacefully at home. Find out on the internet what you'll have to bring along.
Last month I needed to get a parking vignette for our district. AND was quite lucky. Because it has been summer vacation and end of the month, there were less people in the waiting room. In just two and a half hours only (time to drink coffee and read a good book) I was out again and mission accomplished. Wow! What a success!
PS. If you need to know how to register (Anmeldung), see my later post "Bürgeramt Registration"