Use major plot points, truths, and lies to map out your character's arc. And of course, punish them greatly for believing in a lie...
You ask how the change comes about. I think at the extreme it's about survival instinct.
A tragic outcome of the story should represent a death of some sort. It could be physical (as in you're dead-dead), professional (you're fired), or psychological (you're admitted...)
Raising the stakes this high, it's about life and death for your character and they will give their everything to try and change, because you've designed your story in such a way that if they do not, they die.
A character arc is about a character changing his view on a truth vs a lie.
These are some (all?) of the variants:
- Positive arc: The hero goes from believing in a lie to believing in a truth.
- Negative fall arc: The "hero" goes from believing in a lie to believing in a worse lie.
- Negative corruption arc: The hero goes from believing in a truth to believing in a lie (e.g. Anakin Skywalker).
- Negative disillusionment arc: The hero goes from believing in a lie to believing in a truth, but the truth is depressing. (e.g. The Great Gatsby)
- Flat/Testing arc: The hero believes in a truth and the whole world is trying to beat that out of her. (Katniss Everdeen)
You should be telling two stories in parallel about your hero (like two sides of a coin). One story is external and shows the hero's conflict with the antagonist. The other is internal and shows the hero's conflict with himself and his view on the lie vs the truth of the story.
You plot both stories using major and minor plot points, and most information on plot points will give you ideas on how to do this.
Here are some examples of what I mean:
The Midpoint
The most important plot point is the midpoint of the story. This point represents many different things happening at the same time (see James Scott Bell's "Write Your Novel From The Middle" and Stan Williams' "The Moral Premise").
This is the point where your hero (among other things)...
- ...realizes truths about the conflict and the antagonist that will influence him all the way to the climactic moment (the last dramatic scene of the story, the final battle between hero and villain)
- ...makes a decision to follow the truth (happy ending) or the lie (tragic ending)
This happens already in the midpoint because making a decision to change is not the same as having made that change (compare to quitting smoking, starting training, sleeping better, getting an education, you get it...)
Also worth noting: These realizations and decisions do not need to be obvious... the decision could be a small symbolic gesture and the realization could be a sliver of info.
The midpoint also represents a pivotal moment in the story where the information and insights gained will make it possible for the hero to go from being reactive to proactive. Before the midpoint the hero will react to the antagonist's actions while after the midpoint he will start making his own plans.)
Obviously, since we've only come halfway, those plans will fail, and the hero's proactiveness will initially be weak.
Speaking of failing, Jordan McCollum in "Character Arcs" suggests bringing the message/theme/moral of the story through by rewarding the character for following the truth and punishing them for following the lie.
This is optimally done in the outcome of scenes. And since most scenes should have a bad/disastrous outcome, our hero doesn't get much right until the end of the story (the final half of the third act or thereabout).
The Inciting Event
The inciting event (about 1/8 into the story) is the first contact the hero has with the major conflict of the story. This means your hero will have an eight of the book for introduction to the normal world, however, since the inciting event is sometimes rejected, the hero can stay in the normal world longer, trying to stay away from the looming clouds of conflict.
This part of the story is important to get to know the hero, to get to understand what his problems are, and also to show the world that may have given birth to these problems.
The first plot point
About 1/4 into the story comes the first plot point. This is the point of no return that will propel your hero from the normal world into the world of the story conflict. This is when Luke Skywalker's aunt and uncle are killed, leaving him with no reason to stay, this is when Katniss Everdeen is forced to volunteer for the Hunger Games.
The first plot point could be brought about because the character believes in and follows a lie.
However, in Katniss Everdeen's case, it's brought about even though she, being a flat arc character, already believes in a truth. (In the case of the flat arc most problems comes from the world around the character believing in a lie, not the character themselves.)
The third plot point
About 3/4 into the story is the third plot point. This is the disaster that propels the hero from the second act to the third, from initial, fumbling opposition to the antagonist and the lie, to the final showdown. The climactic moment, where the truth triumphs over the lie, or not...
The third plot point should usually come about because of the hero's opposition to the villain. The hero has dared to speak up, take up arms and resist, and this is the villain's revenge. This is also, on the internal level, the point where the lie tries to crush the truth.
The third plot point is also called the dark night of the soul, and it should be dark. It could represent how the hero loses support characters (Obi-Wan is killed by Darth Vader). From now on the hero must take what he has learned and stand on his own legs with no support and no help.
The climactic moment
This is the last dramatic scene in the story (there can be some resolution/new normal world scenes or a chapter of them following the climactic moment, but not much more... perhaps an epilog?)
The climactic moment is the final showdown where the hero fights the villain (in the external plot) and the truth fights the lie (in the internal plot). If the hero decided to accept the truth in the midpoint, the truth should triumph here... though that does not mean the hero must survive (e.g. Gladiator).