Companion abilities require a couple of things, your Inspiration skill will have to be 20 to unlock companion abilities.
The first you'll have access to is Parvati, you can recruit her during the quest Stranger in a Strange Land.
One of the first quests, in the town of Edgewater.
The second companion you can recruit is Vicar Max in Edgewater Vale on Terra 2. You can (it's optional) meet him during the main quest 'Comes Now the Power'. Finish his quest 'The Illustrated Manual' and he will offer to join you. - Thanks AssertionError
The third follower you can find is Felix, departing The Groundbreaker. He will be on the left side before entering your ship.
To use companion abilities you'll simply have to put a crosshair over any enemy in game and press
on the D-Pad. I recommend getting weaker enemies to half health if you want to guarantee the kill.