Ukrainians and their families fleeing from the Russian war of aggression in Ukraine are able to enter Germany freely, without a visa, thanks to the special EU decision (Temporary Protection Directive).
Hence, many people from Ukraine currently do not need a visa if they enter Germany for the first time before 4th of March 2024 (this is the current ruling of the German government very likely to be extended). They do not need a visa or residence permit to stay in Germany legally for up to 90 days from the date they enter. So the last date on which it is possible to be in Germany legally without a visa or residence permit is 2nd of June 2024. In general, the EU Temporary Protection Directive can be extended by EU countries until March 2025, depending on the war developments in Ukraine.
During the 90 days in which you can stay in Germany legally without a visa, you can decide whether you would like to stay in Germany longer. If you decide to stay longer, you have the following options:
Within 90 days of entering Germany for the first time, you can apply for a temporary residence permit under section 24 of the German Residence Law (Aufenthaltsgesetz, AufenthG). Section 24 deals specifically with the situation of refugees from the war in Ukraine based on the relevant EU decision. You can find out here who is eligible for a temporary residence permit under section 24 of the Residence Law, and you can find out more about the procedure here.
Within 90 days of entering Germany for the first time, you can apply for a temporary residence permit for a different purpose, such as to study or work in Germany.
To decide which option would be more advantageous for you, you can make an appointment with the Foreigners´Registration Office (Ausländerbehörde in German) in your area to ask them for advice.