This question is a fairly broad one, and I'm not sure what specific advice you might find useful, so I will just give my perspective of some things to keep in mind, speaking as a person who uses they/them pronouns.
What is a nonbinary person?
A nonbinary person is a person who does not identify as either male or female, and typically does not use male or female pronouns. Instead, they identify as somewhere in the middle, or outside the gender binary entirely. It's a similar concept to being androgynous, genderless or agender, but naturally that's a discussion for another time and I won't get into it.
When you are writing a nonbinary person, here are some general things to keep in mind:
Pronouns, pronouns, pronouns!
Nonbinary people by definition do not identify as either binary gender, and typically use they/them pronouns. However, some nonbinary people do "lean" in one direction and might be okay with those pronouns, too. Your protagonist might be purely nonbinary, or they might lean a bit in one direction, just like bisexual people can lean towards preferring men or preferring women. Think about who they identify as and how they might prefer to lean, if at all.
It's also good to make sure your grammar is cooperating when you write a they/them character, since obviously "they" is a plural pronoun that is used singularly to refer to a nonbinary individual. That can lead to some grammatical confusion in your sentences if you're not careful, so be very cautious and make sure your subjects, verbs and objects agree while using these pronouns.
Misgendering and assumptions
How does your character react to being misgendered or people assuming their gender? Most other nonbinary people I know view being identified by other people as male or female as misgendering and even hurtful, and some may strongly dislike it or have an emotional reaction to it when people do it deliberately or in an offensive way. Personally I don't mind whatever pronouns people call me, and I often make a game of "what's my gender going to be today?" but not everyone is as cavalier as I am, and that's valid, too. Your nonbinary protagonist may have strong responses when people assume their gender or try to invalidate their gender identity, or they might not care at all.
Dead names and previous identities
The concept of "dead-naming" someone in the nonbinary/trans world means that you use the name and pronouns that the person used before transitioning. This is usually very offensive to the person if it's on purpose, and even if it's an accident, for many people it still stings a little.
Did any of your character's friends and family members know them before they accepted themselves as nonbinary and began using a new name and/or pronouns? Do any of their friends and family still misgender or dead-name them? This may naturally cause your protagonist a lot of emotional turmoil and conflict.