To move your character in GoH you must tap on the ground where you want to move.
The character will always move towards the last touch you made on the screen.
To attack - just tap an enemy and your character will automatically attack it with their auto attacks.
If you're a Warrior your character will automatically move towards the enemy to hit it.
If you are a ranged character, the hero will either move to a distance that is equal to their weapon’s maximum range or, if they are already in range, begin firing immediately.
To use an ability tap on the icon. This will activate the ability which will then begin to cool down.
Once the ability is on cool down you can see a dart reset timer counting down until you can use it again.