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).
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 For example, she could become withdrawn or less enthusiastic in class.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.
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.
Another motive could be related to his complex relationship with Dumbledore. Dumbledore might have asked Snape to look out for Draco, and Snape, being obedient to Dumbledore in many ways, would do so to fulfill his request. Also, Snape might believe that protecting Draco is part of a bigger plan to maintain the balance in the wizarding world.
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.
They might face magical justice. In some fanfictions, the Ministry of Magic could get involved and strip them of their magic, or at least put them under strict surveillance.
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.
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.
Snape, being a skilled wizard, could use magic to protect Draco. He might cast protective spells around Draco when he's alone or in vulnerable situations. Maybe he uses a spell that alerts him whenever Draco is in danger, so he can rush to his aid immediately.