The application is conducted via the Campus Management System C@MPUS. We have prepared a manual for the application which you can download here. It will hopefully answer most of your questions. Please read it thorougly!
The application process as well as requirements are described on http://www.uni-stuttgart.de/infotech/application/index.html and the FAQ session http://www.uni-stuttgart.de/infotech/support/faq/index.html
If you still need support contact firstname.lastname@example.org
Deadline for the application is 15-Feb-2017.