Check traffic violations (visit http://www.moi.gov.qa)
Assuming you already cleared violations (if any) and settled payment with buyer
Visit Traffic Dept., or hand over QID to a representative, and bring car Estimara (orig)
Go to typing booths, mention transfer of car ownership
They will type-in details in the MOI form (name, address, etc.) and attach stamp
Go to traffic office, take queue number
Present your document (filled form), your QID, your car Estimara and buyer's QID to the officer
Pay fees by electron card
Officer will issue new Estimara card

Buyer arrange transfer of insurance
Not sure about the cost, approx. QR 90 (70 + 20 for car tint) if I'm not mistaken.

I sold my car two years ago and went through above process. If the procedure has changed, would welcome any information as I intend to sell my other car soon.