Students with EU citizenship do not need a visa to enter Germany.
Citizens of Australia, Brazil, Canada, Israel, South Korea and the USA, for example, do not need to apply for a visa in advance. However, they will have to apply for a residence permit at the City of Fulda's Immigration Office (page only available in German) within three months after arrival. A residence permit that is valid for up to 12 months costs approx €100. A list of all countries and visa requirements can be viewed here.
All students who need to apply for a visa at the German embassy in their home country will be sent an official invitation letter after receipt of their application. After arriving in Fulda, students must register with the City of Fulda's Immigration Office. A representative of the International Office will accompany them.
It takes a few weeks for the new credit card-style residence permits to be issued. You should therefore plan ahead if you need to apply for or extend a residence permit and start the process at least two months before your current permit expires.