Thanks, the formal requirements seem to be a German language certificate like https://www.goethe.de/ins/us/en/sta/ney/prf/testdaf.html and minimum academic requirements for the high school diploma. According to http://anabin.kmk.org/no_cache/filter/schulabschluesse-mit-hochschulzugang.html#land_gewaehlt for example a GPA of 3.0 and new SAT score of 1360 would be sufficient, unless the university itself has a higher requirement.
Assuming that’s all covered, would be nice to read someones actual experience about the application procedure and dealing with the bureaucracy. Also it seems that some more popular German universities require entry exams and interview. See for example, http://www.uni-heidelberg.de/studium/interesse/bewerbung/verfahren/info_satzung.html , which seems to indicate that applicants for certain competitive majors are expected to show up for an interview in August in order to be admitted for fall.