Learn Hardcore Russian: Я ставлю книгу в шкаф. - I am putting the book into the cupboard.

In this sentence, the book is what you are putting, so it must be in the accusative:
Я ставлю книгу в шкаф. – I put the book in the cupboard.

What case is шкаф in, and why does it look like the dictionary form?

Шкаф here is also accusative, because it is the destination of movement (where you are putting the book).

For inanimate masculine nouns like шкаф, the accusative form is identical to the nominative:

Nominative: шкаф – a cupboard
Accusative: шкаф – into the cupboard (after в with motion)

So the word looks the same, but functionally it is accusative.

Why is it в шкаф and not в шкафу?

The preposition в uses two different cases depending on meaning:

В + accusative → motion into something (direction)
- в шкаф – into the cupboard
В + prepositional → location in something (state)
- в шкафу – in the cupboard

So:

Я ставлю книгу в шкаф. – I (am) put(ting) the book into the cupboard.
Книга в шкафу. – The book is in the cupboard.

Movement → в шкаф (accusative)
Location → в шкафу (prepositional)

What does ставлю mean exactly, and how is it formed?

Ставлю is the 1st person singular, present tense of the imperfective verb ставить:

infinitive: ставить – to put, to place (upright)
я ставлю – I put / I am putting
ты ставишь – you put
он/она ставит – he/she puts
мы ставим – we put
вы ставите – you (pl/formal) put
они ставят – they put

So я ставлю corresponds to both I put and I am putting. Russian does not have a separate continuous tense form.

Why use ставить here and not класть?

Russian distinguishes types of “putting” based on position/orientation:

ставить / поставить – to put something upright / standing
- e.g. Я ставлю книгу в шкаф. – I put the book in standing position (on its spine).
класть / положить – to put something lying / flat
- e.g. Я кладу книгу на стол. – I put the book on the table (lying).

For a book in a cupboard, Russians usually imagine it standing on its edge on a shelf, so ставить is natural.
If you clearly meant laying it flat, you would use класть instead, e.g. Я кладу книгу в шкаф. (possible, but a bit less typical unless context makes it clear).

Is ставлю imperfective or perfective, and what would the perfective form be?

Ставлю is imperfective (from ставить).

The perfective partner is поставить:

imperfective: ставить – process, repeated action, general statements
- Я ставлю книгу в шкаф. – I put / am putting the book in the cupboard.
perfective: поставить – a single, completed act
- Я поставлю книгу в шкаф. – I will put the book in the cupboard (and finish doing it).

So, to say I will put the book in the cupboard, you normally use:
Я поставлю книгу в шкаф.

How would I say this in the past tense, and what’s the difference between ставил and поставил?

Imperfective past of ставить:

Я ставил книгу в шкаф. (said by a man)
Я ставила книгу в шкаф. (said by a woman)

Meaning: I was putting / used to put / would put the book in the cupboard (focus on process or repeated action, not on completion).

Perfective past of поставить:

Я поставил книгу в шкаф. (man)
Я поставила книгу в шкаф. (woman)

Meaning: I put the book in the cupboard (and the action is complete). Focus on the result / single finished event.

Does Я ставлю mean I put or I am putting?

It can mean both. Russian has no separate present continuous form like English.

For an action happening right now:
Я ставлю книгу в шкаф. – I am putting the book in the cupboard (right now).
For a habit or regular action:
Я всегда ставлю книгу в шкаф. – I always put the book in the cupboard.

Context (time words, situation) tells you whether it is ongoing or habitual.

Can I drop я and just say Ставлю книгу в шкаф?

Yes. Russian often omits subject pronouns when the verb ending already shows the person and number clearly.

Я ставлю книгу в шкаф. – neutral, fully explicit
Ставлю книгу в шкаф. – still clearly means I am putting the book in the cupboard, slightly more informal or context‑dependent.

Both are grammatically correct. You must keep я only when you need explicit emphasis on I.

Can I change the word order? For example, Книгу я ставлю в шкаф or В шкаф я ставлю книгу?

Yes, Russian word order is flexible, and changes often affect emphasis rather than basic meaning.

Я ставлю книгу в шкаф. – neutral order.
Книгу я ставлю в шкаф. – emphasizes книгу (the object), e.g. It’s the *book that I put in the cupboard (not something else).*
В шкаф я ставлю книгу. – emphasizes в шкаф (the destination), e.g. It’s *into the cupboard that I’m putting the book (not somewhere else).*

All are correct; the neutral and most common version is the original one.

Why doesn’t Russian use anything like “a” or “the” for книгу and шкаф?

Russian has no articles (a/an, the). Definiteness or indefiniteness is understood from context, word order, and stress.

Я ставлю книгу в шкаф. can mean:

I put a book in a cupboard.
I put the book in the cupboard.

If context makes it clear which book and which cupboard you mean, the listener interprets it as the; otherwise, it can feel like a. Russian simply doesn’t mark this difference in the grammar.

What gender is книга / книгу, and why does that matter?

Книга is feminine. You can tell because:

It ends in -а in the nominative singular.
Its accusative singular ends in -у → книгу.

Gender matters because it affects:

Case endings: книга → книгу (feminine pattern).
Agreement with adjectives and past tense verbs, e.g.:
- интересная книга – an interesting book (feminine adjective)
- Я купила книгу. (said by a woman; verb ends in -а for feminine)

Why is it в шкаф and not на шкаф? When would I use на instead of в?

В and на differ in spatial meaning:

в – in / into something (inside a volume):
- в шкаф – into the cupboard (inside it)
- в сумку – into the bag
на – on / onto a surface:
- на шкаф – onto the top of the cupboard
- на стол – onto the table

So Я ставлю книгу в шкаф means you put the book inside the cupboard.
If you say Я ставлю книгу на шкаф, that means onto the top of the cupboard.