Great answer from 'querobles'.

The only thing i would add to his answer is that, if the original owner has a Bank Loan on the car, then go to the bank where the loan is taken from and hand the money over to the bank and NOT the owner. Make sure by speaking to an account manager that the money is being paid in to the correct account to settle the car loan, and make an appointment for two/three days later to collect the No Objection Letter from the bank.

With regard to the insurance, when you negotiate the sale price of the car ensure the remaining insurance is included in the price. Then it is just a matter of going to the insurance company office to transfer the name (should not cost more than QR75 admin fee). Then proceed to the ploice station for transfer of ownership.

Good luck and i wish you lots of safe and hassle free motoring!
:-)