Luffy learned to use Observation Haki only during the two-year timeskip.
He strengthened this Haki by battling Charlotte Katakuri, who had mastered this Haki enough to enable him to see a little bit into the future.
Luffy can now see the future as fluidly as Katakuri, as shown when he helped Hyogoro dodge multiple attacks from Alpacaman and Madilloman before they happened.
Conqueror’s Haki is latent within Luffy, and was first seen used at the Flying Fish Riders’ base to stop the bison Motobaro. Luffy then unintentionally used it in the arena at Amazon Lily, in Impel Down and at Marineford.
Silvers Rayleigh then taught him about this power on Rusukaina, and Luffy trained to use it at will.
Luffy learned also to use Armament Haki during the two-year timeskip.
Luffy is currently attempting to learn an Advanced application of Armament Haki that will allow him to emit his Haki a short distance without a medium.
In the New World, Armament Haki has been a great boon to Luffy’s power.
His Gear Fourth form heavily uses Armament Haki to the point of depleting it in a relatively short amount of time, and while in Gear Fourth, his Haki takes the shape of flames.
The first form, Boundman, makes Luffy’s composition similar to a bouncy ball. He is capable of unleashing blows of devastating power, and he can change the direction of his attacks. His defense also increases, with most attacks bouncing off his body.
The second form, Tankman, makes Luffy much bigger and increases his defensive abilities, allowing him to use them as a weapon via the recoil blasting opponents away.
The third form, Snakeman, is slimmer and focuses on offense. Luffy is granted a tremendous increase in attack speed, and frequently changes the direction of his attacks to assault his opponents from every direction.