One effect is that it can make the story more memorable. When there's a big twist, readers are more likely to remember the story long after they've finished reading it. It also adds depth to the story as it often forces the reader to re - think the events and characters in a new light. For example, a story that seems to be about a simple love affair might turn into a complex mystery with a twist, making the reader realize there were many hidden layers all along.
One way is to mislead the readers. For example, introduce a character who seems to be a hero at first but later turns out to be the villain. Another method is to withhold crucial information until the right moment. Writers can also play with the readers' expectations, like setting up a common plot pattern and then breaking it suddenly.
A great story twist can be found in 'The Usual Suspects'. The ending where it is revealed that Verbal Kint was actually Keyser Söze all along is a masterful twist. It takes the entire story that you've been following and flips it on its head. You thought you knew who the characters were and what was going on, but in the end, you realize you were completely misled.
Zheng Xiyuan, the main character, had once stolen the magic treasure of the Yin and Yang Sect. The Yin and Yang Sect had activated the Dharma Protection Formation to take back the magic treasure. He was about to be teleported away at the critical moment, but he was unexpectedly reborn as the second son of a big family in the foreign world.
One of the best plot twists is in 'The Sixth Sense' where it's revealed that the main character is actually dead. This completely changes the viewer's perspective on all the previous events in the movie.
One good twist could be a character who seems to be the villain turns out to be the hero all along. For example, in a detective story, the suspect who has all the signs pointing to him as the killer is actually trying to protect the real victim from a more dangerous threat.
Maybe the witnesses against the wolf are lying. For example, the pigs could have been the ones who started the trouble, and the wolf was just defending himself. So during the trial, this truth might start to come out, causing a big plot twist.
One interesting plot twist could be that when the big three go back in time, they find out that their actions in the past have unexpected consequences on their present selves. For example, a small decision they make in the past ends up changing their relationships with each other in the present in a major way.
Well, in some fanfictions, a plot twist might be that there's a third party who already knew their identities all along and has been manipulating events. This third party could be using their knowledge to either bring them closer or drive them apart for their own motives. Also, there could be a plot twist where the big reveal is actually a false one, set up by Hawk Moth to deceive them and gain an advantage in his fight against the heroes.