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.