You will need to register at the LaGeSo (Landesamt für Gesundheit und Soziales) and then make an application at the BAMF in order to obtain asylum. Here is some information on the process from the official LaGeSo website: https://www.facebook.com/notes/landesamt-f%C3%BCr-gesundheit-und-soziales/wie-kann-ich-mich-als-asylbewerberin-registrieren-lassen/1646526525672850
I have translated the information into English in case you don't speak German:
If you want to stay in Germany, you first need to register. You need to do this at the LaGeSo. Then you can make an asylum application. You need to do this at the Bundesamt für Migration und Flüchtlinge (BAMF).The registration takes two days. On the first day you will receive a proof of arrival known as an ANKUNA. You will need the ANKUNA to make an application for asylum and to receive help from the state. An official at the LaGeSo will take your fingerprint, take a photo of you and write your name, date of birth, country of origin and first language in the ANKUNA. On the second day you will see a doctor who will check whether you need medical help. After that you can go to the BAMF. This is where you will make your asylum application. You will tell a BAMF official about your experience as a refugee. Then they will check your application and decide whether or not to offer you asylum in Germany. This may take some time.