You can directly apply to the lab of your interest sending them your CV and research proposal. There are few universities where you cannot join directly and you have to go through the graduate admission program, the details, you will find in their website 

 Thank you, Sourav. I'll be very helpful if you kindly provide me little details. 

you can get enquiry from biocuration group www.biocurationssl.com for education consulting 

Hi Sayam, Say if you are interested in Max Planck Institute, you can go to their site and look for the application deadline and process. For ref. please see the following link:

http://phd.eb.tuebingen.mpg.de/information-for-applicants.html

Thank you, Mohammed and Sourav

Each university in Germany has its own rules for PhD. You could check here for Göttingen.

https://www.uni-goettingen.de/en/36700.html

Thank you Nataliya.

Each answer is a variant of the same theme.  If you want to pursue this academic route then you need investigate the website of each institution of interest.  I would assume that every single one of them clearly will outline their requirements for admission.