I'll first refer you to my answer to this question: https://writers.stackexchange.com/questions/24551/how-to-determine-whether-or-not-a-plot-twist-is-needed.
Now I will point out an implication of that answer: a plot twist is a twist back to the story arc. In its essence, a plot twist occurs when a story that seemed to be going in one direction is suddenly revealed to be going in another direction. But that other direction is the direction the story was really going all along. A plot twist is not a story veering off course, but a story veering back on course; a story that seemed to be going wrong suddenly turning and going right.
So the question with a plot twist is not how to turn off the story line, but how to drift off it so that you are then in a position to turn back onto it. For this to seem genuine and satisfying both storylines have to seem plausible, but the true storyline has to be the one that is finally the more satisfying. (By no means does this mean happier.)
To deliberately concoct a plot twist, therefore, (and I by no means believe that they are necessary to make a story interesting) you have to dream up two storylines both of which are plausible extensions of the the same set of events. This implies that (for a plotter, at least) they are planned from the very beginning. When the plot twist comes, it should seem to the reader like a better, more satisfying interpretation of the events that have come before.
In short, if a plot is the instantiation of a story arc, what you need for a plot twist is a single plot that is apparently instantiating one story arc but is later, by some "twist" of events, revealed to be instantiating another story arc.
In this sense, it is not really the plot that has twisted at all. The plot is still a sequence of events, which is all a plot can ever be. It is that readers interpret the events of a plot as instantiating a story arc and expect that story arc to continue. The twist occurs when an event occurs that is incompatible with the story arc the reader has intuited and forces them to intuit a new story arc. The twist is not in the events, but in the reader's interpretation of the events.
Of course, the twist does not occur unless the reader intuits the false story arc rather than the true one. So you need a series of events that very clearly point in the direction of the false story arc, which still making perfect sense as part of the true story arc once the event that forces the change of interpretation occurs.
If you have ever said of some event in a story, "Well, I saw that coming," you have witnessed a case where you as the reader were not deceived by the false story arc the writer was setting up, but saw all along what the real arc was going to be, and were therefore not surprised at all by the "twist" that put the story back on course. If the selling of the false story line fails, the "twist" goes from being the least predictable event of the story to the most predictable. Like everything else in storytelling, it is all in the setup.
From a plotter's point of view, then, it would seem that you need to plan your plots with these two interpretations in mind, making sure that the false is the easier interpretation, but that the true is the more satisfying interpretation of the whole once the clarifying event has occurred.