If I use Team Rocket's Larvitar's "Mountain Munch" attack against my opponent's Team Rocket's Koffing with "Smog Signals" Ability, do they discard the top card of their deck for "Mountain Munch" first or do they get to search using "Smog Signals" first?
The step to check for effects that activate when a Pokemon is damaged by an attack occurs after the step to check for effects other than damage. So the attack effect of discarding their top card is done first, then the triggered effect of searching is done afterwards.
Mountain MunchSmog Signals