He could use his position of authority. Snape might confront the abuser directly. Since he's a teacher, he has the power to intimidate and put a stop to any immediate harm. He could also give Hermione a safe place to stay, like his own quarters (if it's within the rules of the fanfiction world).
The theme of sacrifice also appears. Snape may have to sacrifice his own safety, reputation or his standing within the wizarding world to save Hermione. This shows his selfless side that might have been hidden before. And in some fanfictions, this sacrifice is what ultimately changes the course of the story and the characters' development.
In many fanfictions, Snape saving Hermione from Voldemort can be a very interesting plot. It could be due to Snape's complex character. He was a double - agent in the original series. So, in fanfiction, his loyalty to Dumbledore might drive him to protect Hermione, who is an important part of the good side against Voldemort.
One possible reason could be that Snape sees Hermione's value as a brilliant student. He might recognize her potential and not want it to be wasted just because of her dad's actions or situation. Maybe he has a sense of justice deep down, despite his often cold exterior.
Well, perhaps Snape uses his position as a teacher to step in. He could have been observing the situation secretly and when Draco was about to do something harmful to Hermione, Snape intervened with a firm command or some magic spell to stop Draco in his tracks.
She might use her extensive knowledge of magic. For example, she could brew a complex potion that cures a deadly curse Snape has been afflicted with. Hermione is known for her academic excellence in potions, so it's very likely she'd use this skill to save him.
In many such fanfictions, Snape might notice Hermione's change in behavior. For example, she could become withdrawn or less enthusiastic in class. He's a very observant character, and her academic performance might also start to decline. He could pick up on the signs during one of his patrols when he sees her looking distressed or if he overhears something that makes him suspect she's in trouble.
Well, it could be that Snape has been secretly observing Ron's erratic behavior towards Hermione. When the situation gets out of hand, he intervenes. He might use his position as a teacher to discipline Ron and in the process, saves Hermione. Snape is a complex character with a lot of power and knowledge, so he could use various means like his occlumency skills to sense the danger Hermione is in and act accordingly.
One popular 'snape saves hermione fanfiction' is 'A Different Perspective'. In this story, Snape's complex character is explored in the context of saving Hermione from a dangerous dark magic situation. It delves into his motives which are a mix of his loyalty to the light side deep down and his growing respect for Hermione's intelligence and courage.