Most international students, who are not EU citizens, need a visa to travel to Germany. After their arrival they have to apply for a residence permit which allows them to stay in Germany for the whole period of the MAOT programme (there are exceptions for some other European countries, who are not member of the EU).
The regulations how and when to apply and to receive the travel visa for Germany are different for different countries. Students are supposed to contact the Germany embassy in their home country as early as possible.
The residence permit will be gained after (!) the arrival in Germany. MAOT supports students in receiving that.
Please find more information about visa for the travel to Germany at a page of the German Federal Foreign Office: Visa regulations
Usually it will be necessary to contact the German embassy in your country. Find an overview of all German embassies here (only in German).
If you think of staying longer in Germany than for the duration of MAOT: actual immigration of foreign people or the permission to live in Germany for a longer time is a complicated and long procedure, which needs good preparation and long-time planing. Learn more at a website of the German government about immigration to Germany.