Apparently haki does not always need training to achieve; since we have seen Doflamingo and Luffy awaken it unconsciously. But I heard the Ussop and Ace had the same unexpected, brief "awakening" of conqueror's haki, so when did that happen? Is it also in the manga?
Usopp has awakened his Kenbunshoku Haki which significantly increases the range of his detection radios,during the latter half of the Dressrosa revolt, as he was able to see auras of Luffy, Law, and Sugar, who were in the royal palace, from the old King's Plateau near the Corrida Colosseum. With this, he was able to pinpoint Sugar's location and snipe her down from such a distance. Usopp does not yet have control over it as he just awakened it during his attack to knock out Sugar.
Anime: episode 697
Manga: Chapter 758
It still takes training to use haki but not special training specific to learning haki. For example, you could go around fighting tougher and tougher opponents until eventually, you will accidentally use haki. You could most likely get combat training like Helmeppo and Coby which should result in the usage of haki led straight into haki training since they are being watched by someone. It takes training to master haki although it could be possible to master haki by only fighting stronger opponents and without any guidance but death would be more likely.
he awakened his extended vision on Enies Lobby Arc when giving the keys to Franky and then notices the attacks of the 5 in slo motion