Once you have paid for the car, the person who sold the car to you has to go with you to the police station and present the following documents:
1) Original registration
2) Original ID
3) Old car insurance document with his name on it
4) Car release from bank (this may take up to 5 days for the bank to issue on payment has been made assuming there was a loan involved)

You will need to bring:
1) Your original ID
2) QR 120 in an atm card or visa
3) New car insurance document with your name on it

Once you have all these documents you have to go to an office located at the back of the police station and pay QR 20 to fill a form in Arabic. He will ask for all the documents mentioned above.

Then, once this has been done you just go to the registration section inside the police station.

The entire process should not take more than 20 minutes if you are lucky.