Hostile enemies will attack you as you approach them.
Select an enemy you want to attack by left-clicking on it. When you do, you should see his nameplate and health bar.
Use your abilities to attack the enemy. Abilities appear as icons in the quickslot bar at the bottom of your screen.
To activate an ability, left-click on the icon or press the corresponding number key.
Some abilities do not work if you are out of range. Melee-based abilities can only be used up close, and even ranged abilities have limitations.
As you deal damage, the health bar over the enemy's head drains. When the health bar is empty, the enemy is defeated.