Recently I sold my Car, and the procedure is.

1. Go to the traffic department(Matar Qadeem is better as there wont
be much rush.It the old airport road).
Get the Form filled from a typist.Seller and Byer ID card is
required for this.You have to tell them the phone numbers and
Address of both the parties.(This process will be ove in 10 mins)

2. After filling the form, go to the officer whos doing the process.
Provide them with the ID cards of both the parties along with the
filled application form.
If the buyer wishes to change the insurance type( that is from 3rd
party to full or from full to 3rd party), then that needs to be done
with the insurance agent before going to the traffic department and
the insurance certificate should be provided along with the
application.
If the buyer is opting for car loan, then the buyer should provide a
sponser letter.
If buying on ready cash, then letter is not required.(When i sold
the car, they didnt ask for any letter)
(This process wil be done in 5-10 mins apart from waiting for your
turn)

Thats it...