Knockout (Ex):
At 4th level, once per day a brawler can unleash a devastating attack that can instantly knock a target unconscious. She must announce this intent before making her attack roll. If the brawler hits and the target takes damage from the blow, the target must succeed at a Fortitude saving throw (DC = 10 + 1/2 the brawler’s level + the higher of the brawler’s Strength or Dexterity modifier) or fall unconscious for 1d6 rounds. Each round on its turn, the unconscious target may attempt a new saving throw to end the effect as a full-round action that does not provoke attacks of opportunity. Creatures immune to critical hits or nonlethal damage are immune to this ability. At 10th level, the brawler may use this ability twice per day; at 16th level, she may use it three times per day.
What is the action required to perform said ability? Is it a standard action? Or does it function more or less like stunning fist, where you can use this ability during a full-round attack?
It is a non-action; you just announce that you're using it before making any attack roll for a damaging attack (as opposed to a combat maneuver). You could use it during a full-attack action, sure, though that's not required.
(So yes, just like Stunning Fist.)