Well, if Naruto saves Hinata from Orochimaru in a fanfic, it might start with Hinata being captured by Orochimaru's minions. Naruto would immediately go on a rescue mission. He'd probably fight through Orochimaru's various snake - based defenses. And when he finally reaches Hinata, he'd defeat Orochimaru with a powerful Rasengan, and then carry Hinata to safety.
Often, Naruto's status as a hero in the fanfiction world plays a big role. The Kumo ninjas might be a bit intimidated by him. He might start by making a grand entrance, shouting out his intentions to save Hinata. His reputation precedes him. Then he uses his Nine - Tails chakra, which gives him a significant power - up. He uses this enhanced power to fight off the Kumo ninjas who are holding Hinata captive and finally saves her.
They're popular because fans love the relationship between Naruto and Hinata. Naruto is the hero, and seeing him save Hinata plays into the idea of a classic hero - damsel in distress scenario. It also gives more depth to their relationship.
One popular 'Naruto Save Hinata' fanfiction could be 'The Protector's Promise'. In this fic, Naruto might save Hinata from a powerful enemy during a crucial battle. Another could be 'Naruto's Swift Rescue' where Naruto uses his newfound powers to rescue Hinata from a dangerous situation in a hidden village. And 'Saving Hinata: Naruto's Destiny' might feature Naruto realizing his true feelings for Hinata as he saves her from a life - threatening trap set by the Akatsuki.
In some fanfictions, Naruto might use his new jutsu skills that he's developed in secret training. He could surprise Neji with a powerful Rasengan variant, overpowering him and rescuing Hinata.
The main characters are clearly Naruto, Hinata, and members of the Akatsuki. Naruto is a powerful ninja with a strong will. Hinata is a kind - hearted and brave kunoichi. And the Akatsuki members, who are usually mysterious and have their own motives in the Naruto universe.
In this fanfiction, perhaps Naruto and Hinata are in a dangerous situation. The Akatsuki, which is usually seen as an antagonist group, might have some unexpected reasons to save them. Maybe they realize that Naruto and Hinata are key to some greater good in the ninja world. Or it could be that an individual member of the Akatsuki has a personal connection or debt to Naruto or Hinata that leads to their rescue.
In some fanfictions, Naruto might use his newfound jutsu skills. He could quickly dash in between Hiashi and Hinata, using his speed and agility to block any attacks Hiashi might be launching towards Hinata. His Rasengan in his hand, ready to defend if Hiashi doesn't back down. This shows Naruto's determination to protect Hinata from any harm, even from her own father in this fictional scenario.
Well, it could be that Naruto has developed a new and powerful form in the fanfiction. With this form, he emits an intense chakra that scares off the Cloud attackers who are after Hinata. His speed and strength in this new form are so great that he can easily reach Hinata and get her to safety before the Cloud ninjas can react.
One possibility is that Naruto discovers Orochimaru's lair through some clever detective work. He then sneaks in, avoiding all the traps. When he sees Orochimaru about to perform some sort of experiment on Hinata, Naruto jumps in and starts fighting. He might transform into his Nine - Tails Chakra Mode to gain an edge in the battle and save Hinata.