In the Manga, Haki was introduced in the first chapter. However in the Anime they decided to alih the flashback of seven tahun old Luffy to episode four. So, in the Anime they first introduce Haki in episode 4. Although we don't know that it is Haki, it is used sejak Shanks when he uses Haoshoku Haki against the Sea King that was attacking Luffy. HAki wasn't brought back until episode 151 in which Shanks, once again, uses Haoshoku Haki. This time against Whitebeard's crew. Haki is then brought back once lebih in the Skypia ar. Only this time it is Kenbunshoku Haki, but is referred to as Mantra. Haki then doesn't come back until the Sabaody Archipelago arc, where it is used sejak Rayleigh. after this, Haki becomes a magor factor in the series, being use sejak Rayleigh, Sentomaru, the Kuja Pirates, Luffy himself and many others. It continues to be used without the audience knowing exactly what it is until Rayleigh's explanation of it in episode 516.
I am pretty sure that on Sky Island, what is explained as Mantra can infact be seen as a form of Observation Haki, but the first time it was used i when Shanks saves Luffy, looses an arm, And then uses Conqueror Haki to scare away the Sea creature.