If you are already a resident of the EU - e.g. a UK citizen - you are entitled to live and work anywhere in Germany without a visa. However, you will still need to register with the immigration office (Ausländeramt) and obtain a resident's permit (Aufenthaltserlaubnis).
Similarly, if you wish to work in Germany you will need proof of employment - probably best to take a letter from your employer stating (on headed paper of course!) where and in what capacity you are employed.
For more information have a look at justlanded.com - they wisely advise you not to spend unnecessary time queuing at the immigration offices because you've had to go away and fetch yet another document. Make sure you have it all on the first visit - those additional hours standing in line will never be recouped!
