Well, perhaps Snape could use his authority as a teacher. He might see Ron being too pushy or possessive towards Harry in a romantic sense and intervene by giving Ron extra assignments or detentions to keep him away from Harry.
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 could be the voice of reason. He might see the potential chaos and damage that a romantic relationship between Ron and Harry could cause, not only to their friendship but also to the whole Hogwarts dynamic. So he steps in to prevent it.
Another possibility is that Snape uses his position as a teacher. He might threaten Lockhart with the consequences of harming a student. Given Snape's intimidating presence and his own power within the school, Lockhart would be afraid to cross him. Snape could also call for other teachers to help, making it clear that he won't let Lockhart get away with any harm to Harry.
In this type of fanfiction, Snape could simply intimidate Vernon. Snape has an air of mystery and a certain power about him. He might show up at Vernon's doorstep, give Vernon a cold stare, and with his reputation as a powerful wizard, Vernon might be too scared to oppose him. Snape could then just take Harry without much resistance from Vernon.
In this fan fiction scenario, Snape might use his knowledge of the Muggle world and Vernon's weaknesses. Snape could have found out some information about Vernon's business affairs or personal secrets. Then he blackmails Vernon into leaving Harry alone. By doing this, he effectively saves Harry from Vernon without having to use too much magic and draw unwanted attention.
Perhaps Snape uses magic to create a distraction at the Dursleys' place. He could make strange noises or apparitions that scare the Dursleys, and while they are in a panic, he grabs Harry and disapparates. This would be a quick and efficient way for him to rescue Harry.
Well, in some versions, Ron might use his quick wit and knowledge of Hogwarts' secret passages to outmaneuver Draco. He could lead Hermione to safety through a passage that Draco doesn't know about.
Well, he could use his magic skills secretly. Maybe he casts a spell on the Dursleys to make them docile or distracted long enough to get Harry out. For example, he might use a Confundus Charm on them so they don't notice Harry leaving.
In the fanfic, Snape might use his knowledge of the Dursleys' house layout. He may enter the house unnoticed, find Harry, and then use a Portkey to quickly get them both out of there. He could also have some sort of charm or potion that he uses to counter any magic the Dursleys might have used to keep Harry there, like a spell - breaking potion. And he may have planned the whole rescue very carefully, choosing a time when the Dursleys are least likely to notice, like in the middle of the night.
Well, it could be that Lucius uses his powerful influence in the wizarding world. Maybe he intimidates Ron with threats related to his family's status or he uses some dark magic to create a distraction and whisk Hermione away.