Perhaps Hinata was lured into a trap by Orochimaru who was after her Byakugan. Naruto, being the hero he is, follows her scent or some other clue. He arrives at the scene and has to face Orochimaru's henchmen first. After defeating them, he confronts Orochimaru directly. Naruto uses his Uzumaki bloodline powers in combination with his ninja training to overpower Orochimaru and rescue Hinata.
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.
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.
In a fanfiction where Naruto and Hinata join Orochimaru, one possibility is that they are forced into it. Maybe Orochimaru has some kind of leverage over Konoha that makes them comply. Naruto, being the head - strong character he is, would likely be constantly looking for a way to escape and take Hinata with him. Hinata, on the other hand, would probably be more reserved and observant, trying to find Orochimaru's weaknesses.
Perhaps Naruto teams up with some unexpected allies. For example, he could convince some of Orochimaru's former henchmen to turn against him. These henchmen could provide valuable information about Orochimaru's lair and the security measures in place. Using this information, Naruto can plan a strategic rescue and save Hinata.
In a scenario where Orochimaru kidnaps Hinata, the Hyuga clan would surely get involved. They'd be outraged and use all their resources to find her. Orochimaru might be interested in Hinata's Byakugan for his experiments. He could try to extract its power or study it. But Hinata has been trained in the Gentle Fist style, so she might be able to hold her own against Orochimaru's minions for a while. And who knows, Sasuke might also get involved. He has his own history with Orochimaru and might see this as a chance to confront him again, especially if he realizes that an innocent like Hinata is in danger.
The story could start with Hinata being in immediate danger from the one - tailed beast. Naruto would sense her distress and rush to the scene. He'd face the powerful beast fearlessly. The battle would be intense, with Naruto's agility and strength being put to the test. Hinata, while being protected, could also show her growth and courage. She might not just be a damsel in distress but actively help Naruto. For instance, she could use her chakra to enhance Naruto's abilities for a short time. As the fight progresses, Naruto would gradually gain the upper hand, using his unique skills and the power of friendship to ultimately defeat the one - tailed beast and save Hinata.
Naruto's character development could be shown through his increased sense of responsibility. He is no longer just thinking about himself or his goal to become Hokage. Saving Hinata from Orochimaru makes him realize the importance of protecting those he cares about, which is a big step in his growth as a ninja and a person.
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.
Well, Naruto could potentially be used as a bargaining chip by Orochimaru. Orochimaru might try to trade Naruto for something he wants from Konoha, like secret jutsu scrolls or some kind of political power within the village. And Naruto, being the determined hero he is, would likely be constantly looking for a way to escape and foil Orochimaru's plans.
In some fanfictions, Naruto might go to Orochimaru seeking power. He could be tempted by Orochimaru's knowledge of jutsu. Maybe he thinks that by learning from Orochimaru, he can become stronger faster and be better able to protect his friends and the village.
One possible plot twist could be that Orochimaru was actually being controlled by a greater evil, and Naruto has to not only save Hinata but also deal with this hidden threat. Maybe Orochimaru was forced to target Hinata to draw Naruto out for this other entity's purposes.