When you get close to an enemy, a button prompt will show on the screen with the melee button. Using melee once that icon shows up will trigger a Brutal Melee attack, which is... brutal, as advertised.
NOTE that often I would hit the button and only half the attack would execute, then the game would want me to press the button again to complete it. Because of this, whenever I was trying to melee, I'd just mash the melee button until I knew it was fully successful.