Hi Philip,
Work visa and work permit are almost identical. The work visa you get with a first employer on arrival to germany, sometimes it's bound to this single employer for 2y. At the same time a work permit can also be seen as the work visa but is usually the legal status of your work visa after the 2y when you're free to decide where to work.
How to get a work visa:
It depends if you are in Berlin already or if your Outside of EU in general.
If you're outside you'll need to:
1. Go to the website of the Embassy of Germany in the country you're currently residential
2. Get an appointment for a work visa
3. Fill out all the reuqired forms provided, prepare a notary signed translation of your IDs etc. and take the signed contract with you
4. Go through the procedure and get the work visa
If you're in Berlin (and you don't have a work permit) you'll need to:
1. Go to the website of the "Ausländerbehörde" and get an appointment for a work permit
2. Prepare the documents required, take the contract with you, you're contract for flat, notary signed translated IDs etc.
3. Go there, in the best case take a german friend with you who can help you talking in german
4. Get the work visa or info's on documents you have to provide additionally
If you're in Berlin (and you have a work permit) you'll need to:
1. Check if it's not expoired
2. If it is, follow (2.)
3. if not, do nothing
Links:
Foreign ministry of Germany on the topic of work: http://www.bamf.de/EN/Migration/Arbeiten/arbeiten-node.html
Services of the foreign office in Berlin: https://www.berlin.de/labo/willkommen-in-berlin/dienstleistungen/service.245714.php
General info page for working in Germany: http://www.make-it-in-germany.com/en
Hope this is helpful - with <3 from Berlin :)))))
