shigoto no kaeri ni toshokan de hon o karimashita.

It is read:

しごとの かえりに としょかんで ほんを かりました。

A more natural chunking is:

仕事の帰りに / 図書館で / 本を / 借りました。

仕事の帰りに means on the way back from work or on the way home from work.

Literally:

• 仕事 = work
• 帰り = return, way back
• 仕事の帰り = the return from work
• 仕事の帰りに = on the way back from work

So it is not just work + go home as a full verb phrase. It is a noun phrase meaning the return trip from work.

の links nouns together.

Here, 仕事 modifies 帰り, so 仕事の帰り means something like:

• the return from work
• the way back from work

This is a very common use of の:

• 学校の先生 = school teacher
• 日本の車 = Japanese car
• 仕事の帰り = the way back from work

Here, に marks the time/occasion when the main action happened.

So 仕事の帰りに means:

• when coming back from work
• on the way home from work

This is different from the に used for destinations.

Examples of this kind of に:

• 朝に = in the morning
• 帰りに = on the way back
• 家に帰る = go home

In your sentence, に is not marking where someone goes. It is marking when/in what situation the borrowing happened.

Because で marks the place where an action happens.

The action here is 借りました = borrowed, and that action took place at the library.

So:

• 図書館で本を借りました = borrowed a book at the library

Compare:

• 図書館に行きました = went to the library
  
  • に marks destination
• 図書館で本を借りました = borrowed a book at the library
  
  • で marks location of action

を marks the direct object of the verb.

The thing being borrowed is 本:

• 本を借りました = borrowed a book / borrowed books

So:

• 本 = book
• 本を = book(s) as the object
• 借りました = borrowed

Because Japanese sentences normally put the verb at the end.

A very common basic pattern is:

[time/occasion] [place] [object] [verb]

So here:

• 仕事の帰りに = time/occasion
• 図書館で = place
• 本を = object
• 借りました = verb

That word order is completely natural in Japanese.

借りました is the polite past form of 借りる.

• Dictionary form: 借りる = to borrow
• Polite non-past: 借ります
• Polite past: 借りました

So 借りました means borrowed.

It is polite, neutral Japanese, which is why it is very common in textbook sentences.

Yes. 借りる means to borrow.

This is easy to confuse with 貸す, which means to lend.

So:

• 本を借りました = borrowed a book
• 本を貸しました = lent a book

In a library sentence, 借りました makes sense because the speaker is borrowing the book from the library.

The subject is omitted because Japanese often leaves it out when it is understood from context.

So the sentence could mean:

• I borrowed a book at the library on the way home from work
• He/She borrowed a book at the library on the way home from work

In many beginner examples, the natural default is I, but grammatically the sentence itself does not explicitly say I.

By itself, 本 does not clearly show singular or plural.

So 本を借りました can mean:

• borrowed a book
• borrowed books

Context decides.

Also, Japanese does not use articles like a or the, so those are also supplied by context in translation.

If you wanted to clearly say one book, you could say:

• 本を一冊借りました = borrowed one book

Not exactly.

• 仕事の帰りに = on the way back from work / while heading home from work
• 仕事の後で = after work

So 仕事の帰りに gives a stronger sense of the trip home or the return from work.

If the speaker stopped at the library while going home from work, 仕事の帰りに is a very natural choice.