You should get a German student visa if you are ready to study in a German University. If you’ve been accepted at German University, it is recommended that you apply for a student visa by your self-person at least 3 months in advance before traveling to Germany. With a German Visa, you can travel to nearly 9 different countries in Europe without obtaining visas of these countries

Please note that all your documents and application should be sent to the Immigration Office (Ausländeramt) of your country where you currently residing in. Once your application gets accepted and approved by the Immigration Office, the consulate will issue you a student residence visa. However, once you arrive in Germany, you’ll be required to register.

Required Documents:

A Completed visa application form
Valid international Passport
2 photographs
Admission Letter
Transcript of academic records
Proof that you have sufficient amount to support yourself while living and studying in Germany
Declaration of authenticity of documents submitted

Note that you will also be required to have photocopies of all these documents, get proper insurance and pay an application fee of 60 Euros for the visa.
Where and how to apply?
Read more: http://www.studyabroad365.com/how-to-apply-for-a-german-student-visa/