Citizens of Schengen states do not need a visa to enter Germany.
Citizens of some countries may enter Germany without a visa but need to apply for a residence permit within the first 90 days upon arrival. The list of those countries can be found on the website of the Federal Foreign Office.

Note
You need a visa if you come from a country not listed above.

On the website of the Federal Foreign Office you can find a list of the German embassies and German consulates in your country where you can apply for a visa and get information on visa requirements.

If you intent to study in Germany, you have to apply for a student visa (national visa). As a rule, it is not possible to prolong a Schengen visa in Germany and you are required to leave the country after three months.
Only a few countries are exempt from this regulation. Citizens of those countries may enter Germany for a longer stay without a visa and apply for a residence permit during their stay. The website of the German Academic Exchange Service explains the visa and residence permit requirements for entering Germany with or without visa.

Among other documents you will require the following documents to apply for a German visa:

• Evidence of Evidence of sufficient funds to cover your entire cost of studying and living in Germany; you will be expected to demonstrate funds of 11,208 EUR for one year. For this, you often require a blocked account. This is a special account that is not freely accessible to the account holder.
• Letter of acceptance or confirmation of registration on the study program from the university.

We recommend you to start preparing for your stay in advance, as the visa application procedure can take several months. You can find more information on visa regulations on the website of the Federal Foreign Office.

If you are not a citizen of a Schengen state, you need to apply for a residence permit with the Berlin Foreigners Registration Office after your arrival in Germany. We recommend that you apply as quickly as possible, as it takes 4-8
weeks for the permit to be issued.

After you have successfully completed your studies in Germany, your residence permit can be extended for up to 18 months so that you can search for a job relevant to your qualifications in Germany.

In order to study in Germany, Indian students have to present an APS certificate along with their visa application According to the APS website, the processing can take several months. We recommend you to apply for the APS certificate well in advance, with all the documents that are required failing to which applications can be rejected, even if you don’t have a letter of admission yet.