The game uses a turn-based system where the order of actions in combat is determined by your characters' speed. Beneath the green health bar of each of your characters there is a blue bar which once filled up indicates they are able to act when it is your turn. There will be a circle under your character when it is your turn and three icons signifying their possible actions will appear in the bottom-right of the screen.
The first icon will be the characters' basic attack, the next two icons represent additional attacks or abilities (you can learn more about them by tapping and holding down on the icon). The small rectangular box above each ability must be full before it an be activated. A red crosshairs will now appear on your character’s current target and if you tap the ability you want to activate you will see it play out (sometimes as an animation). If you want to switch to another enemy you just need to tap on the new target. If it is an easy encounter you can tap the icon in the top-left corner of the screen that looks like a fast forward symbol to to automatically play the battle for you.