Each judge counts normally (Unless you are in a stakes class - then I think they average - at least for the money they average - but I'm not positive, never done one) BUT...
Let's say there are four judges and 8 riders in the class.
Judge 1 places you 3rd
Judge 2 places you 6th
Judge 3 places you 4th
Judge 4 places you 8th
The points are awarded depending on the amount of riders in a class. In order for 1st place to earn .5 point there must be 3 riders in the class. In order for 1st place to earn 1 point there must be 5 riders in the class (2nd place would then earn a .5 point).
SO... With the above points the rider would earn zero points. Had there been 10 horses in the class then the rider would have earned .5 points for the third place finish.