Well, in many fanfics, Harry might use his quick thinking and swimming skills. He could have found Hermione using his magical connection to her or by following the signs in the underwater maze. Maybe he used a spell to break whatever was binding Hermione and then swam her back to the surface.
Before needing to be saved, Hermione could be a damsel in distress waiting for Harry. Maybe she got caught by some magical trap set for the second task participants.
One motivation could be simple friendship. Despite being from different schools, they might have developed a bond during the Tri - Wizard Tournament. Viktor could see Harry as a worthy opponent and not want to see him die in the second task.
In the fan fiction, Viktor might use his excellent swimming skills. He is from Durmstrang after all, which is by the Black Lake. He could have swum quickly to Harry when he was in trouble in the water, grabbed him, and swam back to safety.
She could research about the dragons' species and their habits. By knowing what scares them or what attracts them, she can give Harry useful tips. For example, if she finds out that a certain type of music calms a particular dragon, Harry can use that during the task.
Well, he could use his magic skills. Maybe he casts a powerful spell on Ron to stop him and then takes Hermione to a safe place, like Hogwarts where there are protective enchantments.
In this kind of fanfic, one possible scenario could be that Harry uses his quick thinking and magical skills. For example, he might use a stunning spell on the troll just in time to stop it from harming Hermione. Another scenario could be that Harry lures the troll away from Hermione, using his knowledge of the troll's behavior. Maybe he throws something noisy in the opposite direction to draw the troll's attention.
One possible scenario could be that in this fanfiction, Harry discovers that Hermione is being bullied by some dark - minded students at Hogwarts. He steps in immediately, using his skills and the respect he has among his peers to put an end to it. Maybe he threatens the bullies with exposure to the professors if they don't stop.
His courage becomes more evident. By saving Hermione, he shows that he is willing to face great danger for his friend. This act of heroism can make him more confident in his abilities as a wizard.
These fanfics are popular for multiple reasons. First, Harry and Hermione are two beloved characters. Fans enjoy seeing Harry in a more heroic light when it comes to saving Hermione. Also, it allows for different interpretations of the magic world and the characters' abilities. It gives a chance to create new and exciting plotlines based on their existing relationship, like how Harry might use a new spell or strategy to save Hermione. And it can also explore the emotional side of their relationship more deeply, like how Hermione feels when she's saved by Harry.