Basically, a verb changes based on what it's modifying. For the verb "to write," the conjugation looks like
I write We write
You write You (plural) write
He/She/It writes They write
In the English language, it doesn't usually follow a neat, predictable pattern, and the conjugation changes from one verb to the next, which is why you can often tell someone isn't a native speaker by how they write verbs. Also, homonyms and silent letters and odd letter combinations are apt to trip them up. Don't judge them; we have a weird language, okay?
Where most native English speakers run into problems are when you're talking about a group. Though there are many members of a group, as a collective, they're treated as a singular entity. So, say you're talking about a high school football team. You might say, "The players write their papers on the bus whenever they have an away game." Talking about the whole team, though, you'd say, "The coach makes sure the team [it] writes its own homework."
It gets even more confusing when you have a word you're not modifying next to the verb. You'll usually find this to be the case in a prepositional phrase (one that begins with "with," "of," "from," or any of the words on this list.) As an example, let's see another sentence about the football team: "Every member of the team writes his own papers." The verb is modifying "every member," not "the team."
I also want to call your attention to the second half of that sentence, where I wrote, "his." You already know the subject is singular. I used "his" because I'm talking about an all-guy football team. Were this a coed team, though, I'd have to allow for the possibility of the female pronoun. I might write "his or her," which makes the sentence clunkier and more unwieldy.
Grammar rules say I can use "their," which I hate to do. English teachers and grammar experts alike are teaching people that it stands in as a gender-neutral singular pronoun when needed.
I refuse. I will rewrite the first part of the sentence to make it plural before I'll substitute "they" for a single person. I will use the unwieldy "his or her" or even "his/her" before I break out "they" to refer to a single person. I'll also use the already-singular, gender-neutral "one" or "one's," snotty as it makes me sound.
I hope someone finds this useful. High school and college English teachers, feel free to point your students this way.