Talk to Jaucribaix, in Norg on the upper level at the end of the hallway, who will tell you about the ways of a samurai. He requests a Bomb Steel and Sacred Branch and will tell you that if you want to know how to get those items to go talk to his assistants.
Go down the long steps and talk to Aeka, (I-8), who will give you the Oriental Steel. Next talk to Ranemaud, (I-7), who will give you the Sacred Sprig.
Note: If, for any reason, you need to drop either item, you can repurchase them. Aeka will demand one Darksteel Ore for payment, and Ranemaud will want one Platinum Ore and two Gold Ore.
Grab at least one hatchet and go to the far east end of The Sanctuary of Zi'Tah. At K-10 there is a pathway which leads to an unmapped area and L-9. Use your hatchet on a ??? on a huge tree and a Guardian Treant will spawn. Kill the Guardian Treant and trade the Sacred Sprig to the ??? to receive the Sacred Branch.
Next go to point D-8 in Konschtat Highlands and look for the ???. Trade the Oriental Steel to the ??? and Forger will spawn. When killed, Forger will drop the Bomb Steel.
Return to Norg and talk to Jaucribaix. After trading him the Sacred Branch and Bomb Steel, he will inform you that your reward will be ready in 3 in-game days (nearly 3 real life hours).
Return later and speak with Jaucribaix for a cutscene, in which Gilgamesh will hand you your Mumeito and give you the ability to become a Samurai.
Client: Jaucribaix (Near the Captain's Quarters, Norg)
A lump of bomb steel and a sacred branch are required to make a new katana. You will have to ask Jaucribaix's pupils to find out how and where you can get these items.