After getting a job

Einstellungszusage or Stellezusage is the confirmation that a hospital is ready to employ you. Once you get this letter you decide if want to work for this hospital or not. If yes then you contact the hospital with your positive answer and then they'll prepare the contract for you. Most likely they'll send the contract through post, sometimes through email. Same applies for sending your signed copy back to the hospital.

After this you'll have to apply for a residence permit or Aufenthaltserlaubnis. (You may have to apply for Berufserlaubnis or Approbation additionally, since I had the Berufserlaubnis before getting the job my scenario is little different.) If your salary is more than €3300/month, then you can apply for a "Blue Card". If not you have to apply for a normal "Aufenthaltserlaubnis". Two important advantages of a Blue card over a normal Aufenthaltserlaubnis are: in case you lose or quit a job you get 3 months to find a new one; and you get Niederlassungserlaubnis or the German Permanent Residence-ship earlier. Following is a list of documents asked by the Ausländerbehörde regarding this,

1. Contract signed by both you and related person from the hospital.
2. Stellenbeschreibung: Given by the hospital on your request.
3. Contract of the house signed by you and owner.
4. Wohnraumsbestätigung: Ask the owner, form can be downloaded from the website of related Ausländerbehörde.
5. Medical Insurance or proof of its application: You can chose which one you want. You'll need your job contract here.
6. Proof of Application of Rentenversicherung: usually done by the insurance company.
7. Proof of Application of Ärzteversorgung: Every state has its own "Ärzteversorsungskammer" and every doctor has to be a member of it. It can take up to 3 months to get the confirmation of your membership. In Bayern there is a registration fee of €80. Additionally you can also sign something called "Befreiung von der Rentenversicherungspflicht". This basically means that you'll pay your Rentenversicherung to your Ärzteversorsungskammer instead of Deutsche Rentenversicherung. If you sign this then the €80 are levied.

Needless to say that the list varies according to individual application and Ausländerbehörde. Once all the documents are submitted you'll be called for a personal appointment when they'll collect some more of your details, fingerprints etc. The official waiting period to get any sort of card in hand is 3 months. But you can ask for a "Fiktionsbescheinigung" which is issued on the same day and is valid for 3 months. You can start working with this document immediately instead of waiting for the card. With Fiktionsbescheinigung you can also leave and enter Germany in case you have to come back to India for some reason.