Elemental damage deals nature-fire-frost damage, triggers effects that go under the 'shaman', 'fire' 'frost' 'nature' 'magic damage' and 'spell' tags, and will deal your strongest spell school of the three to the target.
This calculation, AFAIK, is carried out in parallel. You're basically throwing an invisible separate frost, fire, and nature spell at the target, and the one that return the greatest number gets used to calculate damage.
Damage is in turn calculate based on the target's vulnerabilities to damage, and Elemental damage presumably hits the resistance that is lowest, then applying the highest single damage% modifiers, then returning a HP damage value.