So, I am going to be running a clone wars campaign and I wanted to get a better understanding on how the ion weapon property worked. I have read the entry for it and it is not clear on how the ion damage is resolved.

Ion damage is applied to the SST of a starship/vehicle or the ST of a droid rather than to the HTT/WT. In effect, it is like stun damage for non-living things. Be aware that starship/vehicle crews can use damage control actions to clear way ion damage to their rides surprisingly quickly and these actions can be repeated as needed in the same scene (unlike repairing damage to HTT). This means that ion damage is a very temporary thing and not nearly as debilitating as it appears to be in the films. Even the ion pulse weapon (Damage 20, Breach 8, Ion) of a Subjugator-class heavy cruiser is really only a tickle that will not compare with what was shown on-screen (and even a handful of damage control crews on a capital ship will wipe away that SS in a mere turn or two).

I believe in the flavor text for ion weaponry that it vaguely says it can disable droids, vehicles and electronics. I'd go with that working however is best for your table, whether it's on-hit, on-crit or works in some other way.