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So when you're in a battle, you see how your characters have icons across the center of the screen, and a number (like 3, 2, 1, 0) in a small circle in the corner? Those character plates are what you use to trigger your unit's special attack. When the counter shows 0 and the background is flashing, that means you can use it. You can long press on the flashing card and it should show you what the unit's special ability is, certain ones have self-heal as the ability.
Also, for those who don't know:
For anyone struggling, you can literally have a maxed legendary team with enough time/determination, because the 1 legendary boosted draw (in the "whirlpool" section of the shop) doesn't cost anything. And you can buy infinite coins and ascension tablets for... nothing. So just spam the legendary draw until you are bursting with units, level up + ascend to your heart's content! And you should be able to easily breeze through the easy stages with a team of even a couple leveled up legendaries.