Often, it starts with the slapping incident which creates immediate conflict. Then, Hermione might be outraged and seek justice or revenge, which drives the plot forward. For example, she could go to Dumbledore about it.
The plot could also develop in a way where the slapping is part of a bigger mystery. Maybe Snape was under the influence of a dark spell when he slapped Hermione, and together they have to figure out who cast the spell and why. This would involve a lot of investigation and cooperation between the two characters, despite their initial animosity.
Often, it starts with Hermione noticing something different about Snape. Maybe she sees a moment of vulnerability or a hidden kindness. Then, she begins to question her previous perceptions of him.
Often, it starts with the introduction of the marriage law. Then, Hermione's reaction to it is shown. It might be shock, defiance, or immediate acceptance depending on the writer's take. For example, if she's against it, she may try to find loopholes in the law.
Often, the plot develops with Hermione constantly being on edge, trying to avoid Snape as much as possible. She might start making excuses to skip classes or meetings where she knows Snape will be present. For example, she could claim to be working on an important research project alone in the library. Meanwhile, she may confide in her close friends like Harry and Ron, but make them swear to keep it a secret.
Hermione may also start to scheme. She'll use her intelligence to come up with a plan. For instance, she might start to collect evidence against Snape, something that she could use to counter his blackmail. She'll research old school rules or find out secrets about Snape that she can hold over his head instead.
Well, it often starts with a lot of misunderstandings. Snape has his own preconceived notions about Hermione as a Gryffindor student, and Hermione has her own view of Snape as a strict and often unfair teacher. However, as they live together, small moments start to change their relationship. For example, when Hermione is having trouble with a particularly difficult spell, Snape doesn't scold her but instead patiently guides her. This gradually builds trust between them, and they form a unique bond that is different from the typical student - teacher relationship or even a normal father - daughter relationship.
Often it starts with Hermione showing an unexpected interest in Snape's area of expertise. For instance, she might ask him for extra help in potions with a bit of a twinkle in her eye and a flirty tone in her voice.
Hermione might initially be very suspicious. Given her intelligence and wariness, she would not easily fall for the temptation. She would likely question Snape's motives and try to analyze the situation from all angles.
In the fanfiction, the relationship may start off with Snape being rather cold and distant towards Hermione as his familiar. However, as Hermione proves herself time and again, perhaps by using her unique skills to solve problems that Snape couldn't on his own, he starts to warm up to her. Their relationship then develops into a more complex one, where they have a mutual respect and a sort of unspoken understanding. This could involve Snape sharing some of his own magical knowledge with Hermione in a way that he would never do with other students, and Hermione in turn, helping Snape with his personal and professional matters, such as dealing with the other Hogwarts faculty or protecting the school from hidden threats.
At first, Hermione might be suspicious of Snape's new - found protectiveness. But as time goes on, she starts to see that he has good intentions. Snape, on the other hand, gradually warms up to Hermione more and more, sharing his knowledge and advice with her.
The story might then focus on Hermione's side of things. She could feel guilty about rejecting Harry and try to be a better friend to him. Or, she might try to set Harry up with someone else she thinks would be a good match for him. Meanwhile, Harry could start to develop feelings for another character as he tries to move on from Hermione's rejection.