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.
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 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 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, 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.
One consequence could be that Harry becomes withdrawn. He's so used to the abuse that he doesn't trust people easily. He might have nightmares often, reliving the moments of abuse. For instance, if Vernon has hit him before, he could have flashbacks in his sleep.
They would likely face severe punishment from the wizarding world. The Ministry of Magic would not tolerate such blatant abuse of a wizard, especially one as important as Harry.
Some fanfictions might depict that the wizarding community might see her as a hero. However, others could show that she faces backlash from some conservative wizards who think she overstepped her bounds. They might try to isolate her at Hogwarts or spread rumors about her. But her friends like Harry, Ron and Hermione would surely support her through it all.
The Dursleys would probably be more frightened. They are muggles and Snape is a powerful wizard. The idea of a strange man in black robes suddenly appearing and using magic would be terrifying for them.
Snape would likely be disdainful towards the Dursleys. He has little patience for Muggles in general, and the Dursleys' mean - spiritedness would not endear them to him. He might use his cold, sarcastic tone on them, leaving them confused and a bit frightened.
At first, Harry might be extremely suspicious. Snape has always been cold and mean to him in the past. He would wonder what Snape's true motives are. Harry is used to being on his own and not relying on Snape for help, so this sudden rescue would be very unexpected.