Some fanfictions depict Hermione using her knowledge of ancient magic. She discovers a spell that can create a portal directly into Harry's room at the Dursleys'. She steps through the portal, grabs Harry, and they both jump back through into a safe wizarding haven. It's really cool because it shows how Hermione's thirst for knowledge can be used to save her friend in unexpected ways.
In a really interesting fanfic, Hermione teams up with Sirius Black (even though he's supposed to be on the run). Sirius creates a diversion outside the Dursleys' house by transforming into his dog form and making a lot of noise. Meanwhile, Hermione uses a spell to unlock Harry's window and climbs in. She quickly disarms any protection spells the Dursleys might have put on Harry and they escape together. It was a great combination of teamwork and magic.
In some fanfictions, Hermione might use her intelligence and magic skills. For example, she could use a powerful spell to create a distraction at the Dursleys' place. Maybe a spell that makes all the dishes in the kitchen start flying around, causing chaos. Then, while the Dursleys are distracted, she could quickly grab Harry and apparate away to a safe place, like the Burrow or a hidden wizarding location she has prepared in advance.
The Dursleys might be left in a state of shock and confusion. Since they have been so mean to Harry, they could be worried that the wizarding world will come after them for revenge. But since they are Muggles, the wizarding world may just leave them be, but they will always live in fear of the unknown.
In some fanfictions, Ron saves Hermione from Bellatrix in a more psychological way. He manages to get into Bellatrix's head, using a rare mind - influencing spell. He makes Bellatrix see her worst fears, which causes her to drop her wand and flee, leaving Hermione unharmed. This shows that Ron doesn't always have to rely on brute force to save Hermione. It also adds an interesting layer to his character as someone who can be clever and resourceful in different ways.
In this fanfiction scenario, Bellatrix saving Harry from the Dursleys is quite an unexpected twist. It could be that Bellatrix has some ulterior motive. Maybe she wants to use Harry for her own dark purposes against Voldemort. She might see Harry as a valuable pawn in the power struggle within the Death Eater ranks.
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).
One possible plot could be that Voldemort realizes Harry's importance in a different way. Maybe he sees that Harry has some power or knowledge that could be useful to him in the long run. So, instead of wanting to kill Harry, he decides to rescue him from the Dursleys to gain his trust and manipulate him later. For example, Voldemort might think that Harry has a connection to some ancient magic that only he can access, and by saving him, he hopes to get access to it through Harry.
Well, perhaps Fleur uses her Veela charm to intimidate the Dursleys into letting Harry go. She could arrive at Privet Drive in a blaze of magical beauty and power, and the Dursleys, being the cowards they are, would be too scared to oppose her when she demands Harry come with her.
One thing that could happen is that the wizarding world would be in chaos. The Death Eaters would be confused by Bellatrix's actions, and the Order of the Phoenix would be very suspicious. Harry would be in a difficult position, not knowing whether to trust Bellatrix or not.
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.
Maybe Percy uses his magic skills to create a distraction. He could conjure up some strange creatures outside the Dursleys' house. The Dursleys, being afraid of all things magical, would be distracted long enough for Percy to sneak in and get Harry out.