In the world of Nickelodeon's “Avatar the Last Airbender,” the Avatar is a being of immense power, reborn into each generation to maintain the balance of power in the world. He is capable of bending each of the four major elements of air, earth, fire and water, which means he can control them using martial arts. The Avatar is the only character with this ability; others can only bend a single element, if they are benders at all. While the Avatar is born with these latent abilities, he must master the elements and master the Avatar state before he can gain the power needed to perform his task.
Master the bending skill of the nation into which the Avatar was born. In the show, Aang is born into the Air nation and masters air bending at a temple school. It is there that he is determined to be the Avatar reborn. Each successive Avatar will be born into a different nation, so the first element learned will be dependent upon that.
Travel to the three other nations and locate a master who can train you. Aang found Kitara of the water nation, Toph of the Earth nation and Zuko of the fire nation. These three children were masters of their element and traveled with Aang to teach him. If you are playing a game based on the show, this will be your quest. If it is only based on the mythos and not the story line, you'll need to find masters on your own.
Practice all four of the elements until you learn them well. Even after mastering these abilities, however, you will not have attained true Avatar power. Mastering the Avatar state is required to commune with past Avatars and gain their power and insight.
Open the seven chakras to allow your energy to flow throughout your body unimpeded. This will allow you to achieve the Avatar state. The seven chakras are Earth, Water, Fire, Air, Sound, Light and Thought. They are opened by releasing the emotions that block them. The emotions you need to free yourself from are fear, guilt, shame, grief, lies, illusion and earthly attachment. When you can master the elements and your emotions, you will achieve the power of the Avatar.
The martial arts styles of the four nations are based on actual styles. The Airbenders use a style called Ba Gua Zhang; the Waterbenders use Tai Chi; the Earthbenders use Hung Gar; and the Firebenders use Northern Shaolin.