If you have fled to Germany, you should register with authorities such as the Federal Office for Migration and Refugees (BAMF), the Foreigners' Registration Office ("Ausländerbehörde") or the police post at your Initial Reception Centre ("Ankunftszentrum"). It might be the case that you have been already registered at the German border or in your first place of arrival in the country. In any case, you will be registered as a refugee, and your fingerprint and some other personal data will be recorded. This process is called PIK ("Personalisierungsinfastrukturkomponente"). You will then receive proof of arrival ("Ankunftsnachweis").
In principle, not only fugitives but all those who come to Germany and want to stay longer than three months, have to register ("Anmeldung") their residential address with the German authorities after two weeks. Even if you are not a refugee, you still must contact local authorities such as "Einwohnermeldeamt" or "Bürgeramt", as the Federal Registration Law (BMG) specifies.
After registration, you should apply for a Residence Permit at the Foreigners' Registration Office ("Ausländerbehörde"). You can read more about four different forms of protection for refugees in the Right of Residence chapter. For more information on how to apply for asylum, see the Asylum Procedure chapter.