If you wish to study in Germany, you will need a visa for entry (residence permit). Students from EU member states and from states with which special agreements have been made don't need a visa. For more information click here (official list of visa requirements by country).
Basically there are two different types of Visas.
1. The Schengen-Visum is valid for a short stay of less than 3 months within a 6 month period. This means that you cannot use this kind of visa when you wish to study in Germany for more than 3 months.
2. The Nationales Visum is for a stay of more than 3 months.
The Visa must be requested and issued before your arrival in Germany by a German Consolate or Embassy. In order to recieve a Visa, you must have a valid passport and proof of financial self-sufficiency for the duration of your study in Germany. Additionally, you must either have proof of acceptance (Studierendenvisum), valid for accepted students, or a certificate of your status as an applicant (Studienbewerbervisum), valid for not yet approved applicants. Authorization for a visa can take many months. Plan far in advance and be sure that you have all of the required information when applying.
The student visa (Studierendenvisum) will be issued if you have already been accepted by a German university. The study applicant visa (Studienbewerbervisum) permits you to enter the country before the admission decision by the university. This visa may also be useful to applicants who wish to improve their language skills in Germany before starting their studies. The study applicant visa is limited to three months, but it can be converted to a student visa if you receive your admission from the university during this period. A language course visa (Sprachkursvisum) is only for the duration of the course and cannot be converted into a student visa.
Please note that you cannot study on a tourist visa, and a tourist visa cannot be converted into a student visa.
Further Information: