Firstly, you send your application according to the law for severely disabled persons (Antrag nach dem Schwerbehindertenrecht). Fill it out and send it by mail to:
Landesamt für Gesundheit und Soziales Berlin
(Berlin State Office for Health and Social Affairs)
Versorgungsamt
Postfach 310929
10639 Berlin
Enclose a copy of your identification document and your residence permit (e.g. the certificate you received after filling out the online application form). You will then receive a confirmation of receipt. Current medical findings, discharge reports, expert opinions, etc. are required to further process your application. If these are not available, you will have to visit the relevant doctors or hospitals in Germany. If your documents are not in German, they must be translated and certified – the authorities cannot pay for this, nor can they translate the documents for you.
At the moment, the application procedure usually takes 5 months. After looking at all documents, the Berlin State Office for Health and Social Affairs will give you a ruling on the degree of disability. If your degree of disability is 50 or higher you will receive a Disability Card