Snape is a very intelligent and resourceful character. In the fan fiction, he could have enlisted the help of some of his allies in the wizarding world. For example, he might have asked a friendly house - elf to create some chaos in Vernon's house. While Vernon is distracted by the chaos, Snape can easily find Harry and take him to a safe place. Also, Snape may have used some potions to make Vernon temporarily incapacitated so that he can't harm Harry.
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.
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.
It could be that Snape wants to spite Vernon. Vernon represents everything that Snape despises about Muggles who are cruel and unaccepting. By saving Harry from Vernon, Snape is showing his superiority over Vernon and also his power as a wizard. And of course, there's still that underlying reason of his love for Lily which makes him want to protect her son.
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.
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.
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.
Perhaps Dudley finally stands up to his father's cruel treatment of Harry. Maybe he realizes that Vernon's behavior towards Harry is wrong and uses his own physical strength or some clever ruse to get Harry out of a difficult situation Vernon has put him in.
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.
If Snape witnesses Vernon abusing Harry in fan fiction, he might use it as an opportunity to gain some leverage over Harry. Snape could offer to keep quiet about the abuse in exchange for Harry doing certain things for him, like getting good grades in Potions. However, this is a rather cynical view and goes against Snape's more complex character who deep down has some good in him.
In this fan fiction, Snape's character development is quite remarkable. At first, he might be hesitant and conflicted about saving and adopting Harry. But as time goes on, he becomes more selfless. He has to learn to communicate better with Harry, which is a big change for him. He also has to face his own demons from the past, like his relationship with James Potter. This journey of self - discovery and growth makes his character more three - dimensional and likable in the context of the fan - made story.
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.