How to Write Thoughts in your Fiction Writing
I like to think that quality writing is mostly technique and patience (duh). In fiction, style is a huge determinant of the piece's mark on its readers.
When it comes to formatting exactly how to write out the words expressing characters' thoughts, it can depend on how what tone the overall work has and what traits the character has. It also must match the point-of-view you've chosen.
Say you have an orphan with grit, yet is very resourceful. You may also want to imbue their relentless mindset to approaching their environment into every word you use. Add in that you chose the first-person point-of-view (maybe even the particular and challenging stream-of-consciousness?!). Then what you'd likely need is this sort of format for most of your character's thoughts:
Mariah's lip curled at his naivete. Even in the smallest games clueless children stir themselves into have stakes; why would any of the rest of the world not live with this unavoidable truth? Complaints can only get you under the boot of the more powerfully greedy.
Can you guess where thought and narration differ? Where does each begin then end? Taking a guess could also be another sort of game (hehe) you might want your readers to engage in.
There are a few frequently used ways to format thoughts, very similar to how to format speech:
Dizzy, he pulled the doctor close, so close that all he could see was his teeth, so white, so blindingly white, so blindingly beautiful, and to those teeth, which were the closest thing in the room to God...
Shaona was puzzled, thinking how a baby could injure her teacher's health.
He thought, "What if I just buy more batteries to keep for blackouts?"
In the first example, we have what can be a direct thought, but it could also be the narrator mixing their style of narrating with the character's actual words to tell us what and how they think. If the word "thought" was there, we arguably wouldn't be comfortable assuming that this is exactly how he thought at the moment; we'd be open to assuming that the writer's own language was used to tell what was happening. However, we're getting an intimate look at the character's...character. Or just the intensity of their emotions. This is what many experts and nonexperts call, the free indirect style.
We get psychology by having this more direct format, a closer look at any inner conflict, and the pattern of thought (if the writer consistently uses this format).
Specific and careful diction (syntax + vocabulary) also makes the person's expression in real life, after all. Currently, fiction writers would likely use this, but this statement may not even be true anymore--the diversity in literature today is so much more apparent than it seemed twenty years ago.
The writer uses reported or indirect speech in the second example. For most realistically styled narratives, this type of format dominates because we're kept apart from the character's unfiltered thoughts so that we can also discern how they are connected to what's happening around them. The emphasis here is that connection and engagement with the world instead of the purer expression of their thoughts and effects of interactions.
The third example is in direct/quoted speech. This is an older style of writing out thoughts that allows and it's largely gone out of style because of its odd separating the character into 2 by its handling of the language of thought versus event-narration. Is he talking to himself out loud, or do his thoughts literally have sound and material depth in his mind? Ar they like persons themselves? (Actually, that's pretty cool.)
Bottom line, how you write out your character's thoughts must be kept consistent with how you wish to relate conflict and what kind of conflicts they will have. What's the emphasis on, expression, competition, or a little bit of both? The same goes for writing out speech--notice how all the examples I gave had the word "speech" as their terminologies? Don't forget to let yourself ponder on what you want your readers to know, feel, notice, and how they will do all of these things and you will have a great project to share with the world!