You probably require a student visa for Germany. You should apply for this via the local German embassy or consulate in your home country. The typical fee for a visa is €60.
The require documents generally are:
Completed application form
Letter showing you’ve been accepted by a German university
Transcript of academic record
Certificate of German language proficiency or proof that you intend on attending a language course in Germany (if studying in German)
Proof that you have sufficient funds to support yourself while living in Germany (€8,700 per year, which is roughly ~US$9,390)
Certificate showing you’ve purchased health insurance
Declaration of authenticity of documents submitted
If you’re intending to stay in Germany for more than 90 days, you should apply for National Visa with the purpose being study rather than a Student Visa, as it allows you to stay in Germany for 3 months.