Kad završim, stavit ću knjigu natrag na policu.

Both kad and kada mean when.

• kad is shorter and very common in everyday Croatian.
• kada is a bit fuller and can sound slightly more formal or emphatic.

So Kad završim... and Kada završim... are both correct here.

This is very normal in Croatian.

After kad meaning when, Croatian often uses the present tense to talk about a future event, especially with a perfective verb.

So:

• Kad završim... = When I finish...
• not literally present-time When I am finishing...

English often uses present in this kind of clause too: When I finish, I’ll put the book back...

So Croatian and English are actually behaving similarly here.

Because in Croatian, after kad in a time clause like this, you normally do not use the future tense.

So the natural pattern is:

• Kad završim, stavit ću...

not

• Kad ću završiti...

Using ću there would sound unnatural in standard Croatian for this meaning.

Završim is the 1st person singular present form of the verb završiti.

So:

• završiti = to finish
• završim = I finish

Because završiti is a perfective verb, its present-tense forms often refer to a completed future action in sentences like this.

That is why Kad završim means When I finish.

The full infinitive is indeed staviti.

In the Croatian future tense, there are two common patterns:

• Ja ću staviti knjigu.
• Stavit ću knjigu.

In the second pattern, when the infinitive comes right before the auxiliary ću, the final -i is dropped:

• staviti + ću → stavit ću

So stavit ću is a normal future-tense form meaning I will put.

In standard Croatian, it is written as two words:

• stavit ću

not

• staviću

Writing it as one word is associated with Serbian spelling, not standard Croatian spelling.

So for Croatian, stavit ću is the form you want.

Because knjigu is the accusative singular form, and the book is the direct object of stavit ću.

• knjiga = nominative, the dictionary form
• knjigu = accusative, used for the thing being put somewhere

Compare:

• Knjiga je na stolu. = The book is on the table.
• Stavit ću knjigu na stol. = I will put the book on the table.

Because Croatian distinguishes between:

• movement toward a place → usually accusative
• location in a place → usually locative

Here, the book is being moved onto the shelf, so we use na + accusative:

• na policu = onto the shelf

If the book were already there, you would use na + locative:

• na polici = on the shelf

So:

• Stavit ću knjigu na policu. = I will put the book onto the shelf.
• Knjiga je na polici. = The book is on the shelf.

Natrag means back.

So without natrag:

• Stavit ću knjigu na policu. = I will put the book on the shelf.

With natrag:

• Stavit ću knjigu natrag na policu. = I will put the book back on the shelf.

It tells you that the book is being returned to its previous place.

Often yes in everyday speech, and people would understand you.

• natrag = back
• nazad = back

However, natrag is often preferred in standard Croatian, especially in careful writing. Nazad is very common in speech, but some teachers or textbooks may prefer natrag.

Because Croatian usually does not need subject pronouns when the verb form already shows the person.

Here:

• završim already means I finish
• stavit ću already means I will put

So ja is unnecessary unless you want emphasis or contrast.

For example:

• Kad završim, stavit ću knjigu natrag na policu. = neutral
• Kad završim, ja ću staviti knjigu... = more emphasis on I

Croatian word order is fairly flexible, but not completely free.

This sentence is very natural:

• Kad završim, stavit ću knjigu natrag na policu.

You could also hear variations such as:

• Kad završim, knjigu ću staviti natrag na policu.
• Kad završim, stavit ću natrag knjigu na policu. — possible, but less neutral

The most natural order is usually the one that keeps the sentence clear and unmarked. The version you have is a very good standard one.

Because ću is a clitic. Clitics are short unstressed words that normally cannot stand alone at the beginning of their clause.

So Croatian prefers:

• stavit ću knjigu...
• ja ću staviti knjigu...

not

• ću staviti knjigu...

That is why, after Kad završim, the main clause starts in a way that gives ću something to attach to.