I think you’ll understand that the answer to this question is depending on your personal goals in Germany. Do you want to learn German just for survival in Germany’s everyday life? Or do you plan to study at a German university in a German study program.
1. Survival in Germany
Like in any place in the modern world, you can get your money from the cash machine, shop in self service stores and get the rest done with international sign language. That means, you’ll survive in Germany even without any knowledge of German. If you speak English, you’ll also find a lot of people that’ll understand you, especially amongst younger population.
Anyway I’d recommend to learn at least some basic German, because very soon you’ll recognize, that you cannot get all things done without words and that not everyone in Germany is speaking English at any time. Or to say it in German: The tendency to speak English (and any other foreign language) is dwindling with every beer. If you know what I mean.
So what does a basic level of German mean? Although my experience tells me, that communicative talent is varying considerably amongst language learners, I would say that the basic level for survival German is corresponding roughly to the level B1 of the Common European Framework of Reference for Languages (CEFR).
A short description of language skills corresponding to level B1 you can find in the global scale of the CEFR. But let it put me in my words: With B1 you’ll not understand too much, what people say, but you can express most of your desires in a very simple way and most of the people will understand you.
2. Studying in Germany
If you want to study in Germany, you are lucky, because you do not need to bother your head about how much German you should learn – your university will tell you what level of German you’ll need to apply for your study program.
By the way: Did you know that German universities nowadays offer a lot of study programs in English language? If you plan to study in an English study program usually you will not have to present any proficiency in German to enter the university and you can go back to point 1.
If you want to study in a German study program, you’ll have to pass a German language exam before starting your studies. Please notice, that this does not mean any German language exam. You’ll need to pass one of the language exams, that are accepted by German universities.
The most commonly known German language exams for university admission are TestDaF and DSH. (For more info on TestDaF and DSH look here) To pass one of these exams it is usually recommended to have German language skills on level C1 of the CEFR.