Learn Hardcore Finnish: Minä juon kahvia ja luen kirjaa samaan aikaan. - I drink coffee and read a book at the same time.

You are drinking an unspecified amount of coffee (not a clearly defined portion like “the cup of coffee”).
The action is seen as ongoing / not completed.

So:

Minä juon kahvia. = I am drinking (some) coffee.
Minä juon kahvin. = I drink (finish) the coffee (a specific, whole portion).

That -a marks the partitive and gives the idea of “some coffee / coffee (in general)” rather than “the whole coffee.”

Why is it kirjaa and not kirja?

Kirjaa is also partitive singular, from kirja (“book”).

Here the partitive suggests:

You are in the middle of reading the book, not finishing it within the time frame you’re talking about.
The book is not thought of as a completed, whole object of the action yet.

Compare:

Luen kirjaa. = I am (in the process of) reading a book.
Luen kirjan. = I (will) read the book (through to the end).

So kahvia and kirjaa work the same way here: both are partitive objects, giving a sense of ongoing, partial action.

How would the meaning change if I said “Minä juon kahvin ja luen kirjan samaan aikaan”?

That sentence is grammatically correct, but the nuance changes:

Minä juon kahvia ja luen kirjaa samaan aikaan.
→ I am (at the same time) drinking some coffee and reading a book.
→ Focus on activities in progress.
Minä juon kahvin ja luen kirjan samaan aikaan.
→ I (will) drink the coffee and read the book (both as complete tasks) at the same time.
→ Focus on completing two whole tasks.

The second version sounds a bit unusual in everyday speech because it implies you manage to finish an entire coffee and an entire book “at the same time.” It’s more natural with things that can realistically be completed in the same time span, or when you’re planning tasks:
Luen raportin ja kirjoitan vastauksen samaan aikaan. – “I’ll read the report and write the reply at the same time.”

Can I leave out Minä and just say “Juon kahvia ja luen kirjaa samaan aikaan”?

Yes.

In Finnish, subject pronouns (minä, sinä, etc.) are often dropped, because the verb ending already shows the person:

Juon = I drink / I am drinking
Luen = I read / I am reading

So:

Juon kahvia ja luen kirjaa samaan aikaan.
is perfectly natural and very common.

Including Minä adds a bit of emphasis:

Minä juon kahvia ja luen kirjaa samaan aikaan.
→ I (as opposed to someone else) drink coffee and read a book at the same time.

Why don’t we need a word like “am” in “I am drinking”? How does Finnish express that?

Finnish has no separate “am/is/are + -ing” structure like English.

The simple present tense in Finnish usually covers both:

English simple present (“I drink”)
and present continuous (“I am drinking”).

So:

Minä juon kahvia.
can mean either “I drink coffee” (habitually) or “I am drinking coffee (now)”, depending on context.

In this sentence:

Minä juon kahvia ja luen kirjaa samaan aikaan.
would naturally be understood as
“I am drinking coffee and reading a book at the same time (right now).”

What exactly are juon and luen? How do they relate to juoda and lukea?

Juon and luen are both:

1st person singular present indicative forms of the verbs
Dictionary forms: juoda (“to drink”), lukea (“to read”)

Patterns:

juoda → juon (I drink / am drinking)
- stem juo-
  - -n (1st person ending)
lukea → luen (I read / am reading)
- stem luke- changes to lue-
  - -n → luen
- the vowel change is a regular type of stem alternation in Finnish.

The -n ending marks “I”; that’s why the pronoun minä is optional.

What does “samaan aikaan” literally mean, and how is it formed?

Samaan aikaan means “at the same time.”

Breakdown:

sama = same
aika = time
samaan = “into the same” (illative case of sama)
aikaan = “into (the) time” (illative case of aika) – but in this fixed phrase, it appears as aikaan in some contexts and simply aikaan / aikaan merges into aikaan / aikaan, with samaan aikaan being the usual everyday form.

As a fixed expression:

samaan aikaan = “at the same time, simultaneously”

You can use it widely:

He nauravat samaan aikaan. – They laugh at the same time.
Teemme sen samaan aikaan. – We’ll do it at the same time.

A common synonym is yhtä aikaa.

Does “samaan aikaan” apply to both verbs, or only to “luen kirjaa”?

Even though samaan aikaan is placed at the end, it is naturally understood to modify the whole combination of actions:

I drink coffee
and (I) read a book
at the same time

So the meaning is: both drinking and reading are simultaneous activities.

If you wanted to stress that only one of the verbs is “at the same time” relative to something else, you would usually rephrase or reposition it, or add more context. But in this simple sentence, listeners will assume the adverbial belongs to both actions together.

Can the word order be changed? For example, can I say:
“Juon kahvia ja luen kirjaa samaan aikaan” or
“Minä juon kahvia ja samaan aikaan luen kirjaa”?

Yes. Finnish word order is fairly flexible, and all of these are possible:

Minä juon kahvia ja luen kirjaa samaan aikaan.
Juon kahvia ja luen kirjaa samaan aikaan.
Minä juon kahvia ja samaan aikaan luen kirjaa.
Samaan aikaan juon kahvia ja luen kirjaa.

The default, neutral version is like 1 or 2.
Versions where samaan aikaan is earlier (3–4) can give it a bit more emphasis (“at the same time, I drink coffee and read a book”), but the basic meaning stays the same.

Why are there no words like “a” or “the” for “a book / the book” or “coffee” in the Finnish sentence?

Finnish has no articles (no direct equivalents of a/an or the).

Instead, information that English expresses with articles is conveyed by:

Case endings (e.g. partitive vs accusative)
Word order
Context

In this sentence:

kahvia → “(some) coffee / coffee” (indefinite, mass)
kirjaa → “(a) book / (some of a) book” (indefinite, ongoing)

If you wanted to be more “definite,” you would normally use context or a different case, e.g.:

Juon sen kahvin. – I drink that coffee / I’ll finish that coffee.
Luen sen kirjan. – I’ll read that book (completely).

But there is still no separate word for “the”; definiteness is implied, not directly marked with a standalone word.

Is it possible (or natural) to repeat minä with both verbs, like “Minä juon kahvia ja minä luen kirjaa samaan aikaan”?

It’s grammatically correct, but in normal speech it sounds heavy or over-emphasized.

Natural Finnish normally uses one subject shared by coordinated verbs:

Minä juon kahvia ja luen kirjaa samaan aikaan.
or just: Juon kahvia ja luen kirjaa samaan aikaan.

Repeating minä is used when you want strong emphasis or contrast, for example:

Minä juon kahvia ja sinä juot teetä. – I drink coffee and you drink tea.
Or: Minä juon kahvia ja minä luen kirjaa samaan aikaan! (insisting that you really do both).

So: correct, but usually only for special emphasis.