These are traditionally measured just by a ruler. You can put a ruler under the plate and measure how many mm across each clear zone is. You could also put the plate on graph paper in the same way. Since the clear zone is clear, you can see what is underneath. (or you can invert everything and look at it from the bottom of the plate). There is nothing special about how this is done.
In addition, measuring the zone of inhibition could be trick. I have carried out some methods using ruler and you have to be careful your starting line.
If you measure across the zone, your answer should be divided by two.
Please not that the clear zone is only taken as the inhibition zone.