Foundations
It is worth researching at the beginning of your studies whether you are eligible for a foundation's funding programme.
Extracurricular and voluntary work are just as important as above-average performance at school and university. Your profile should also match the foundation.
As a scholarship holder of a foundation, you will generally receive financial support for stays abroad, similar to the bafög abroad (Auslandsbafög), with the difference that you do not have to repay the scholarship!
You can find an overview of all state-funded foundations at: www.stipendiumplus.de
There is also the Federal Association of German Foundations. It lists all German foundations, some of which also award scholarships to students.