Counterattacks are primarily seen in PK and PvP (the Arena). Any time that a fellow PC uses a skill, they will either start flashing a reddish-orange aura (as characterized by their display portrait also doing the same) or a solid lime-green aura. Using R1 (Rengeki) at this moment and executing a skill will perform a counterattack. You'll probably obtain a bulk of these from the PvP battles needed to advance the story, but if you are hunting the PK targets in Battle Fields, you may also get some points accredited to your overall score by doing it there too.