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.
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.
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.
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.
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.
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.
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.
He might use his speed and stealth. For example, if they are held in a guarded fortress, Naruto could use his incredible speed to quickly take out the guards one by one without being noticed. Then he can find Ino and Hinata and get them out safely.
Well, one possible plot could be that Hinata gets caught in the crossfire during a battle involving the One Tail Beast. Naruto, being the hero he is, rushes to her rescue. He might use his Rasengan or some new jutsu he's developed to fend off the beast and save Hinata. Maybe Hinata was on a mission to gather information about the One Tail and got in over her head.
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.