Go to the Traffic Dept. and make an appointment with Ahmed, a likeable Saudi who walks very fast. It's always on a tuesday at 'Dalla' somewhere downtown (don't bother trying to find it yourself - you won't - and get a Saudi Car), be there early (7ish would be appropriate). Either pay the fees online before or bring cash, make sure you have pictures and a legible English translation of your driver's license or they will reject you for sure (= happened to an American). Be patient!
The driving test itself is fun and explains a lot what you will see in terms of driving in and around JED...