Learn Hardcore Finnish: Kirjoitan uuden sanan sivun reunalle. - I write a new word in the margin of the page.

Kirjoittaa is the dictionary form (the infinitive, “to write”).
Kirjoitan is the 1st person singular present tense form: (minä) kirjoitan = “I write / I’m writing.”

Do I need to include minä (“I”)?

No. Finnish usually drops the subject pronoun because the verb ending already shows the person.

Normal: Kirjoitan uuden sanan sivun reunalle.
Emphatic/contrastive: Minä kirjoitan... (e.g., “I will write it, not you.”)

Why does uusi become uuden?

Because the adjective must agree with the noun in case and number, and uusi has an irregular stem change when declined.

Base form: uusi sana (“a new word”)
In this sentence’s object form: uuden sanan

So uuden is the declined form of uusi that matches sanan.

Why is it uuden sanan and not uusi sana?

Because uusi sana is the nominative/basic form. Here, a new word is the (complete) direct object of the verb, so it takes the “total object” form, which in the present indicative looks like genitive singular:

(Minä) kirjoitan uuden sanan.

If you used the basic form uusi sana, it would not match standard object marking in this context.

Is sanan genitive or accusative here?

Formally, sanan looks like the genitive singular of sana. Functionally, in Finnish object grammar it’s often described as the accusative-like total object (because Finnish doesn’t have a distinct accusative form for most singular nouns).
So you’ll see it explained either way:

“Genitive object” (common in teaching)
“Total object (accusative function)” (more grammatical/functional description)

What’s the difference between writing uuden sanan vs uutta sanaa?

It’s the classic total vs. partial object distinction:

uuden sanan (total object): the action is seen as completed / whole (you write “the whole word”).
uutta sanaa (partitive): the action is ongoing, incomplete, or not bounded, or it can imply “some new word” in a less definite sense.

In many everyday situations, kirjoitan uuden sanan sounds like you’re writing down a specific word as a complete item.

Why is it sivun and not sivu?

Because sivun is the genitive form meaning “of the page.” It modifies reuna (“edge/margin”):

sivun reuna = “the page’s edge” / “the edge of the page”
So sivun is not the object of the verb; it’s a possessive/relational modifier of reuna.

What case is reunalle, and what does -lle do?

Reunalle is in the allative case (-lle), which typically expresses movement or direction onto / to / toward something:

reuna = edge
reunalle = onto/to the edge (the margin)

Here it indicates the “destination/location” of the writing: you write the word onto the margin.

Could I say sivun reunassa or sivun reunaan instead?

Yes, but the meaning changes:

sivun reunassa (inessive -ssa) = “in/at the page’s edge area” (location, no movement implied)
sivun reunaan (illative -Vn) = “into the edge” (often feels less natural here; illative is more like “into/inside,” though with some nouns it can mean “into the area of”)
sivun reunalle (allative -lle) = “onto/to the margin” (very natural for writing onto a surface/area)

For writing on a margin, reunalle is usually the most idiomatic choice.

Is the word order fixed? Could I rearrange the sentence?

Finnish word order is flexible, but changes emphasis.

Neutral: Kirjoitan uuden sanan sivun reunalle.
Possible alternatives:
Sivun reunalle kirjoitan uuden sanan. (emphasizes where you write it)
Uuden sanan kirjoitan sivun reunalle. (emphasizes what you write)

The case endings keep the roles clear even when you move parts around.