Thankfully, those days are now gone. You can get to know the fine pending against your name sitting in the comfort of your home. If you are having a SAWA mobile phone (as most expats do), just type your iqama number and sms it to 88993. It would cost you SR1.5 and you will get a reply back in your mobile about the pending fine. If you are a Mobily subscriber, just type your iqama number and send an sms to 625555. You can also call 01-2928888 through your landline to know the status of your fine. Just follow the instructions after dialling this number.
Once you know the fine amount, you have to go to either Al Rajhi Bank or Riyad Bank and pay the same. You can also do it online if you have an account in either of these two banks.
Talking about fines, I always used to wonder how some people just get away with all that rash driving? I never realized it until I saw it myself. Believe it or not, with the right 'wasta', you CAN get your fine amount reduced! I have never seen such a thing anywhere else in the world! In the earlier days, people even used to get their tickets cancelled before it was entered in the system, but now it has become a bit difficult.
Rather than undergo all of this, the best way would be to just drive safely and reach home in one piece! Hope this information was useful.