You can register as an asylum seeker at a border authority, police station, foreigner’s registration office ("Ausländerbehörde") or an initial accommodation centre for refugees ("Erstaufnahmeeinrichtung"). You just need to say the word "asyl" (or "asylum"), and the staff would know what you mean. After announcing that you want to apply for asylum, you would be considered an asylum seeker. Then you would be taken to an initial accommodation centre for refugees to register. Or, you may receive a document and a ticket to go to such facility on your own. The document mentioned above is called "Anlaufbescheinigung", and it shows that you have done the initial registration as an asylum seeker.
Registration as an asylum seeker
How do I register as an asylum seeker in Germany?

Every refugee who comes to Germany has to go to the relevant German authorities and register- this is called "Asylgesuch". "Asylgesuch" is an initial -but necessary- registration to notify the German state that you want to apply for asylum in Germany. Then, you should go to BAMF and officially apply for asylum. It is after submitting this application that your asylum procedure will start.
Registering as an Asylum Seeker
Important
If you have moved to an apartment or have been transferred to another accommodation centre, you must notify the Foreigners' Registration Office ("Ausländerbehörde") and the Federal Office for Migration and Refugees (BAMF) about your new address. Otherwise, you will not receive your letters and may miss crucial dates or deadlines.