Becoming a Ninja on Club Penguin is rather easy. Here I will bring you through a very helpful guide in which you will have less difficulties becoming a Black Belt Ninja on Club Penguin.
First off:
To become a Ninja, You have to earn belts by playing a game called Card Jitsu. Card Jitsu is located at the dojo which is on the map. When playing do not use the blue mats on the floor, it takes longer to earn each belt if you play that way. Simply walk up to Sensei and Play in Competition mode. That's the fastest way to earn belts.

Card Jitsu:


At The Dojo, players are given a deck of cards by the Sensei. Every turn, players choose one card from their hand. Players then compare symbols: Fire melts Snow, Water extinguishes Fire, and Snow freezes Water. The player with 3 different color combination's first, wins.




When Playing this game Keep in mind:



Each game you win, the higher you move up in levels. Complete all levels and become a Black Belt ninja. To reach a Black Belt you have to earn 8 other belts before - Starting with white and ending with brown.
Here is the amount of wins you approximately have to have to gain a belt:

White belt : 5-7 wins
Yellow belt : 7-13 more wins after white.
Orange belt : 8-14 more wins after yellow.
Green belt : 9-15 more wins after orange.
Blue belt : 10-16 more wins after green.
Red belt : 12-17 more wins after blue.
Purple belt : 13-18 more wins after red.
Brown belt : 11-19 more wins after purple
Black belt : 10-20 more wins after brown