Learn Hardcore Finnish: Tämä on muistikirja, johon kirjoitan uusia sanoja joka ilta. - This is a notebook in which I write new words every evening.

Finnish doesn’t have articles. Whether you would translate it as a notebook or the notebook is usually inferred from context.
In Tämä on muistikirja, the demonstrative tämä (this) already makes it specific enough in many situations.

Why is it Tämä on muistikirja and not something like Tämä on muistikirjan or Tämä on muistikirjaa?

After the verb olla (to be), Finnish typically uses the nominative for a normal identification statement:

Tämä on muistikirja = This is a notebook.

Other cases can appear with olla, but they change the meaning:

Partitive (muistikirjaa) can suggest “some/not fully/at the moment” in certain contexts, but it’s not the default for simple “X is Y” identification.

What exactly is muistikirja? Is it a single word?

Yes, it’s a common compound noun:

muisti = memory
kirja = book
So muistikirja is literally a memory book, i.e. a notebook.

Why is there a comma before johon?

Because johon kirjoitan uusia sanoja joka ilta is a relative clause that adds extra information about muistikirja. Finnish normally separates relative clauses with a comma:

muistikirja, johon… = a notebook, into which… / that I write in…

What does johon mean, and why isn’t it joka?

johon is the relative pronoun joka (which/that/who) in the illative case (roughly “into which / where (into)”).

Finnish puts the needed case ending on the relative pronoun:

joka = which/that (basic form)
johon = into which / where (into)

Why is johon in the “into” form? I’m writing in a notebook, not into it.

Finnish commonly treats “writing in a notebook” as “writing (things) into a notebook,” so the notebook is seen as a container receiving text:

kirjoittaa johonkin = to write into something
So johon matches that pattern.

(You’ll also see kirjoittaa jonnekin / kirjoittaa johonkin used similarly with other “destination” places.)

Could I use mihin instead of johon?

Not here. mihin means (to) where? and is used in questions:

Mihin kirjoitat? = Where do you write (into)?

In a relative clause referring back to muistikirja, you use the relative pronoun form:

muistikirja, johon… (not mihin)

What form is kirjoitan, and why is it used?

kirjoitan is:

verb: kirjoittaa = to write
form: 1st person singular, present tense = I write

Because the sentence says this happens joka ilta (every evening), present tense works for a habitual action:

I write (there) every evening.

Why is it uusia sanoja and not uudet sanat?

uusia sanoja is partitive plural, often used for:

an indefinite amount (“some new words”)
ongoing/repeated actions (you’re regularly adding words, not completing a fixed set)

uudet sanat (nominative plural) would sound more like:

“the new words” as a specific, complete set, depending on context.

So kirjoitan uusia sanoja is the natural way to say “I write down new words.”

What are the dictionary forms of uusia and sanoja, and how do they change?

Dictionary forms:

uusi = new
sana = word

Forms in the sentence:

uusia = uusi → partitive plural (new (some), plural)
sanoja = sana → partitive plural (words (some))

They agree in number and case: both are partitive plural.

How does joka ilta mean “every evening”? Why isn’t it a plural form?

joka ilta is an idiomatic time expression:

joka = each/every
ilta = evening

Finnish often uses the singular in “every X” time phrases:

joka päivä = every day
joka viikko = every week
joka ilta = every evening

It functions as an adverbial meaning “on each occasion of that time unit.”

Is the word order flexible here? Could I move joka ilta?

Some movement is possible, but it changes emphasis. Common options:

…johon kirjoitan uusia sanoja joka ilta. (neutral: “every evening” added at the end)
…johon kirjoitan joka ilta uusia sanoja. (slightly more emphasis on the routine: “every evening I write…”)

Both are natural; the original is very typical.