How did naruto become the sixth hokage?

Answer 1

Actually, he hasn't.

After the Akatsuki's invasion of Konoha, Tsunade fell into a coma after using an excessive amount of chakra. During a council member, the three Elders proposed a new Hokage be set immediately, saying that there was no way to tell when the Godaime was going to wake up.

The one chosen was Danzo, former rival of the Third Hokage, Hiruzen Sarutobi. However, I don't believe that he is counted very highly, as his reign was only temporary. (He used a self-sacrificing jutsu known as Izanagi against Madara and Sasuke Uchiha.)

When news of Danzo's death reached the Council's ears, they began trying to find a new Sixth Hokage. Therefore, Kakashi Hatake, former student of Minato Namikaze, the Fourth Hokage, was the one chosen. He was just about to accept when a lower-ranking ninja interrupted the ceremony, saying that Tsunade Hokage had awoken from her comatose state.

Although Naruto is the protagonist of Naruto, it doesn't actually mean that he'll become Hokage. Though it'd be nice if he could rise to that status, he is sure that a prophecy about him is that he will die fighting is ex-teammate, Sasuke Uchiha.

Further more, if you go back in time, then you will realize that Naruto wanted to protect his "precious people", no matter what the cost.

Answer 2

Danzo became Hokage at the end of Naruto manga chapter 450.

Answer 3

Danzo was the 6th Hokage for about 5-9 episodes. Then he was killed and now kakashi is the hokage (unofficially tho.)