i think you can apply at every police station. Or at the LAGeSo (Landesamt
für Gesundheit und Soziales). Address: Turmstr. 21, 10559 Berlin.
After that the Bundesamt für Migration und Flüchtlinge (BAMF), the
ministry for refugees, is responsible for you. There you will send your
asylum application. At first you might be asked for personal details,
photographed, fingerprinted, and be asked 25 questions about yourself
and how you got to Germany. Your answers will be recorded and used
later in your big interview.
Please correct me, if I understood something wrong.