Each fight consists of a series of turns, which keep repeating until you either win, or lose. The fight starts with a Player turn, which is you: first, you can use your team to attack the opponents.
Each of your heroes can strike once during the turn (you decide the order in which they strike). You strike by selecting the opponent(s) you want them to attack from the 5x5 grid, then click on the Attack button.
Each strike, damage is calculated based on the attributes of the attacker and defender: this damage (if any) is substracted from the HP of the opponent. When that reaches 0, the opponent is defeated, and removed from the playfield.
Once all your heroes are done (or you press the done button), the Opponent Turn starts. During this turn, each remaining Opponent will choose a hero to attack, and strike her/him. The damage is calculated based on the attributes, and (if any) substracted from the HP of your hero. Once that reaches 0, the hero is defeated.
This cycle repeats until either all opponents, or all heroes are defeated.