Nondialogue voice or your character's inner voice is usually done in a way that aligns with how the character speaks with the rest of the characters in the story. But sometimes an author wants to show that a character has extra depth or perhaps isn't who they appear to be to the reader or other characters in the story.
Using character voice as exposition may seem like a simple technique, but more often than not, writers do this in a heavy-handed way. This leaves their dialogue stilted, dry, and an obvious story function that drains their prose. Blending story exposition and important story information allow you as the writer to keep your story engaging while feeding your reader what they need to know to stay grounded in your story and characters.
Once you've found your character's voice, how do you deepen it to make it memorable and engaging? This is the second biggest hurdle a lot of writers face. They've found that cool voice and they're like 'Great! I'm done.' But going the extra step to develop, deepen, and shape that voice around your story can create an even richer voice and engaging dialogue throughout your story.
While there are tons of ways of discovering your characters' voices, the basic idea behind all of them comes down to one thing: figuring out how your characters speak in a variety of situations related to who they are, where they're from, and who they are speaking to. Think about it. Do you talk the same to every one you speak to? What about characters in your favorite books? Do their voices stay static throughout the whole story?