Non-EU nationals will have to apply for a Student Visa (“Visum für Studienzwecke”). As the regulations governing the issuing of visas may vary according to country, you will have to get in touch with the German Embassy in your home country to find out about requirements. It is recommended that you get general information on how to apply for a student visa well in advance of the date you wish to take up studies, as applying for a visa and the visa application process can take some time. In some cases student visa applicants may have to wait for three or more months before getting the final decision.
It is generally not advisable to enter Germany with a tourist visa, (unless you are specifically instructed to do so by the German Embassy responsible for the issuance of your visa) because it cannot be changed into a residence permit for studies, not even if you are in possession of the admission certificate to a German university. In such a case you would have to return to your home country!
The visa process in general goes like this: The German Embassy office, where international applicants apply for a visa, will send the application directly to the Aliens Registration Office of the town in which you wish to reside. The Aliens Registration Office then has a deadline for issuing a statement (for the Embassy) with regard to the application.
Once you are in Germany, you will receive more information on how to extend the visa at the Aliens Registration Office (“Ausländerbehörde”). In most straightforward cases, the International Office of Saarland University can assist you directly on campus, you will probably not need to go to the main Aliens Registration Office.