Perhaps Naruto has some sort of premonition about Sasuke's danger. He follows his gut feeling and finds Sasuke trapped by Haku. He then uses his Uzumaki bloodline power, something that might be enhanced in fanfiction, to disrupt Haku's chakra flow and save Sasuke.
In many fanfictions, Naruto's save can be a complex and emotional event. Naruto could first try to reason with Haku, appealing to his humanity if there is any. When that fails, Naruto might recall all the training he has done with Kakashi and the promises he made to himself and Sasuke. He then combines his basic ninja skills like the Shadow Clone Jutsu in a new and creative way. For example, he creates a distraction with the clones while he sneaks up on Haku through the blind spots of the ice mirrors. Once he gets close enough, he uses his physical strength to break Haku's hold on Sasuke and get them both out of harm's way. This whole process is often filled with Naruto's internal monologue about his friendship with Sasuke and his determination not to lose him.
One possible scenario in this fanfiction could be that Naruto discovers Haku and Kimimaro in a dire situation. Haku, with his ice techniques, and Kimimaro, with his powerful bone abilities, are perhaps being overpowered. Naruto, being the hero he is, jumps into the fray. He may convince them to change their ways and join him in Konoha, as he once did with Sasuke. This would not only show Naruto's growth as a ninja but also his ability to bring out the best in others.
Well, in the fanfiction, Naruto could save Ino from Sasuke by appealing to Sasuke's former friendship. Naruto might talk to Sasuke, reminding him of their days in Team 7 and how Ino is also their comrade, which makes Sasuke change his mind and let Ino go.
Simple. Naruto is a hero at heart. He can't stand seeing anyone being hurt, especially his friends. Ino is his friend, so he has to save her from Sasuke.
Naruto might develop a deeper understanding of the power of friendship and how it can cross enemy lines. His act of saving Haku could make him more determined to see the good in everyone. For Haku, he could start to question his loyalty to Zabuza and consider a different way of life, which is a significant character development.
The first key element is Naruto's understanding of Sasuke. He knows Sasuke's past, his pain, and his motives. This understanding allows him to approach Sasuke in a way that can reach him. Second, the role of the ninja world around them. The village's values, the other characters' opinions, all can influence Sasuke's journey. For instance, if the village shows forgiveness and acceptance, it can be a factor in pulling Sasuke back from the dark. And finally, the internal struggle within Sasuke. There's the part of him that wants to be saved by Naruto and the part that is consumed by darkness, and this struggle is central to the fanfiction.
Well, in one possible scenario, Sasuke might be under some sort of dark influence. Naruto, being the hero he is, senses Hinata is in danger from Sasuke. Naruto arrives just in time, using his newfound powers, perhaps a combination of Sage Mode and his Nine - Tails chakra. He blocks Sasuke's attack aimed at Hinata and then tries to reason with Sasuke, reminding him of their past friendship and how Hinata is an innocent bystander. Eventually, Sasuke relents and Hinata is saved.
Well, in the fanfiction, Naruto might use his speed and agility to whisk Sasuke away from the fangirls. Maybe he creates a diversion, like using a clone to draw the fangirls' attention while he grabs Sasuke and flees to a safe place.