Applying for a scholarship is possibly the best known way to gain financial support as a student. Scholarships are granted e. g. by many funding organisations, as well as politically-affiliated foundations, religious institutions or business-related organisations.
When it comes to international exchange, the German Academic Exchange Service ("Deutscher Akademischer Austauschdienst", or "DAAD" for short) is one of the most important German institutions. Here, German and international students and scientists on most levels of academic qualification can apply for financial support in many different funding programmes.
The DAAD offers an extensive scholarship database, which you can use to search the funding programmes of the DAAD and many other funding organisations to find a scholarship that suits your needs and requirements:
DAAD Scholarship Database
Important scholarship providers besides the DAAD are the 13 Stipendium Plus organisations ("Begabtenförderungswerke" – unfortunately, the overview is currently only available in German) for the promotion of young talent, or the Deutschlandstipendium, for which you can apply at most universities in Lower Saxony.