Well, in some fanfic scenarios, Voldemort might have made a deal with someone who has access to the Dursleys' house. For example, he could have bribed or threatened a neighbor or someone who works in the area. Then, when the time is right, he enters the house under the guise of this person's help and rescues Harry. It could also be that Voldemort has some sort of inside knowledge about the protective spells around the Dursleys' place. He finds a loophole in those spells and slips in to save Harry.
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.
At first, Harry would probably be extremely confused and distrustful. He's been told all his life that Voldemort is the bad guy. But as Voldemort continues to protect him from the Dursleys, Harry might start to question what he knows. He could gradually become more open to listening to Voldemort's side of the story.
There's also the idea of envy. Voldemort might envy the normal life that Harry could have had if not for the wizarding world's interference. By saving Harry from the Dursleys, he is both taking Harry away from a life he could never have himself and also trying to create a new situation where he can be in control of Harry's life, rather than the Dursleys or the Order of the Phoenix.
Daphne could be a fictional character created specifically for this fanfic. She might be a witch from a well - known wizarding family. Maybe she's a classmate of Harry's at Hogwarts or someone who has just heard about his situation and feels compelled to help.
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.
Perhaps he realizes that Harry has potential that can be used for his own purposes rather than just killing him. So he wants to keep Harry close and away from the Dursleys who are just muggles.
After saving Harry, Snape may have to deal with a lot of mistrust from some people in Hogwarts who don't understand his motives. However, he might also start to form a closer bond with Harry, which could change the whole dynamic between them. This new relationship could lead to some unexpected alliances and enmities within the wizarding world. And if the Dursleys were to try and retaliate, Snape would have to constantly be on guard to protect Harry from any potential harm they could cause.
Well, perhaps Daphne somehow discovers Harry's awful situation at the Dursleys. She might use magic to break into the house secretly. Then she could use a spell to make the Dursleys forget about Harry so that she can take him away without a fuss.
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.