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.
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).
Snape would probably be very stern with Draco. He might give him a severe scolding and deduct points from Slytherin. Snape is a strict teacher and he won't tolerate such behavior from his own house students.
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.
Well, it could be that Draco, in his pure - blood pride and influenced by his family's views, targets Hermione. Maybe he uses some dark magic or just plain bullying. Snape, despite his often cold exterior, might save her because he secretly admires Hermione's intelligence or perhaps he has a deeper reason related to his own past with the Gryffindors or his hidden loyalties. For example, he could see a bit of himself in Hermione's determination to succeed in a world that is often against her.
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.
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.
Draco might be motivated by jealousy. He could be jealous of Ron and Hermione's friendship or a possible romantic relationship between them. So he tries to harm Hermione out of spite.
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.