Because Morris is such a grammar technician, ze didn't want to use they/them as nonbinary pronouns because they/them are typically plural pronouns, meaning more than one person. So, as an alternative, Morris uses ze/zir, which function like he/him or she/her but don't have any gender attached to them.
Here's how to use ze/zir pronouns:
Ze is the non-gendered equivalent of he/she.
-Ex. (m.) He likes coconut candy.
-Ex. (f.) She likes coconut candy.
-Ex. (z.) Ze likes coconut candy.
Zir is the non-gendered equivalent of him/her.
-Ex. (m.) The test got the better of him.
-Ex. (f.) The test got the better of her.
-Ex. (z.) The test got the better of zir.
Zirs is the non-gendered equivalent of his/hers.
-Ex. (m.) The wallet is his.
-Ex. (f.) The wallet is hers.
-Ex. (z.) The wallet is zirs.
And zirself is the non-gendered equivalent of himself/herself.
-Ex. (m.) He took himself to the movies.
-Ex. (f.) She took herself to the movies.
-Ex. (z.) Ze took zirself to the movies.
Ze/hirs is also a non-gendered option (Ze, hir, hirs, hirself), but Morris (really me, the author) chose ze/zir because it has more distinct sounds and harder to misunderstand as gendered pronouns. That's just zirs (my) personal opinion and if you feel differently, that's okay! Just remember it's the nonbinary person's choice on what they want people to use for them, and you have to respect that! Even if the nonbinary person uses they/them, that's valid too, even if it's not technically grammatically correct. Times are changing, and literature is slow to catch up, so the proper pronouns for nonbinary people is still up for experimentation.