Well, it could start with Hermione being in a vulnerable situation, like being cornered by the troll in a dark, damp dungeon. Harry, being the brave hero, arrives just in time. He might first distract the troll by conjuring up some annoying little creatures that the troll would start chasing. Then, when the troll's back is turned, Harry would grab Hermione and apparate them both to a safer place, like the Gryffindor common room.
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 plot twist could be that the troll is actually under the control of a dark wizard. So when Harry saves Hermione, they realize that there is a much bigger threat at hand. Another twist could be that the troll turns out to be a transformed Hogwarts student, and they have to find a way to reverse the spell instead of just fighting it.
One reason could be that the troll is simply on a rampage and Hermione was in the wrong place at the wrong time. Trolls are not known for their intelligence, and it might have just stumbled upon Hermione while wandering the Hogwarts halls.
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.
Well, in many such fanfictions, Harry might use his magic skills. He could cast a powerful stupefy spell on the troll to stop it in its tracks and then quickly lead Hermione to safety. Maybe he also uses his quick thinking and knowledge of the Hogwarts corridors to find a hiding place where the troll can't reach them.
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.
They're popular because the relationship between Harry and Hermione is so strong in the original series. Fans love to explore scenarios where Harry gets to be the hero specifically for Hermione. It shows the depth of their friendship and loyalty.
One great 'Harry Potter Saves Hermione' fanfic could be 'The Rescue in the Forbidden Forest'. In this fic, Harry uses his advanced magic skills he's secretly been practicing to fend off dark creatures that are attacking Hermione. Another one might be 'Harry's Swift Intervention', where he arrives just in the nick of time to save Hermione from a dangerous spell gone wrong during a duel. And there's also 'Saving Hermione from the Abyss', which has a really intense plot where Harry has to brave many obstacles to reach Hermione who is trapped in a magically created abyss.
Adventure is also a common theme. The scenarios in which Harry saves Hermione usually involve some sort of adventure, like exploring dangerous places or facing powerful dark forces. For example, in some fanfics, they might be in an old, abandoned castle full of traps and curses, and Harry has to fight through all that to reach Hermione.