She might start by using her knowledge of Naruto's past. Since she is his mother, she knows things about his early life that no one else does. She could use these memories to create an emotional connection with him. Maybe she'll show up in his dreams first, like a hazy memory, and then gradually reveal herself in the real world.
The fanfiction might change the important events in his life in a way that he doesn't like. For example, if it rewrites how he became a ninja or his relationship with his teacher, Iruka. These are fundamental parts of his story, and if they're distorted in the fanfiction, it's understandable that he'd get angry.
In fanfiction, Naruto could get the Byakugan through some sort of experimental jutsu gone wrong or right. Maybe a scientist ninja was trying to combine different kekkei genkai and it ended up giving Naruto the Byakugan.
He might get paid in ryo. Some rich clans or individuals who want to see the chaos might offer him a sum of ryo for each successful prank he pulls on a particular clan.
At first, Naruto would likely be very angry and hurt. He's always wanted to be accepted in his village, and banishment would feel like a huge rejection. But he's also a fighter. So, he'd probably channel that anger into getting stronger. He might have moments of self - doubt, but his determination would push him forward.
Well, in some fanfictions, Naruto might get the Buster Sword through a special encounter. Maybe he stumbles upon it during a mission in an ancient ruin. Another possibility is that it could be given to him by a powerful ally who has connections to the world where the Buster Sword originally comes from.