You are not required immediately to register as a war refugee and apply for a residence permit for temporary protection. You are allowed to stay in Germany legally without a visa until the end of August 2022. However, if you wish to stay longer, work or need social benefits, you have to register and apply for the temporary residence permit (Aufenthaltserlaubnis).
For this, the first step is to report to the Arrival Centre at the former Tegel Airport. The Arrival Centre will check whether you can stay in Berlin or whether you will be allocated to another German federal state. If you have relatives in Berlin, or you have found permanent accommodation or a job, you will generally be allowed to stay. If you are allocated to Berlin, you will also be registered immediately at the Arrival Centre. Among other things, your fingerprints will be taken and photos will be taken of you.
Subsequently, you can apply for a temporary residence permit online. You can access the online application here. After you have filled out the application, you are allowed to work and apply for social benefits.