Talk to Cougar Gai to signup for the quest. He will ask you to bring a message to Field Cat Joe in Einbroch.
After you come back from Einbroch, you will need to give him the above items to finish off the quest and become a Ninja. Be sure to checkout the other NPCs in the Ninja Guide, they are your source for ninja gears.
How to get to Einbroch: Take the Izlude airship (1200z). Exit at Yuno. go downstair into the terminal, talk with the Airport Staff to take the airship to Einbroch. Exit at Einbroch.
He will ask you to help him gather the above items then he will help you find Field Cat Joe. After you show him the items, he will reveal himself as the person you are looking for. He will give you a reply, take the items off you and warps you back to Amatsu.
Note: It is best to collect double the amount of what he asked for since Cougar Gai will ask you to bring him the same thing later.
Now you are supposed to go back to Cougar Gai. As mentioned above you have to bring him the same set of items Joe asked for. So just give him the items and be ready to be transformed into a Ninja! He will give you an Ashura to start off as a Ninja.