Learn Finnish: Kirja maksaa yhdeksänkymmentä euroa.

It is a compound word! It is made by combining yhdeksän (nine) and kymmentä (a form of the word for ten). So it literally means 'nine tens'. All the 'tens' words in Finnish from 20 to 90 are built this exact same way.

Why does the sentence use euroa instead of euro?

In Finnish, any number greater than one requires the noun that follows it to be in the partitive form. Euroa is the partitive singular form of euro.

I remember maksaa meaning 'to pay'. Does it mean 'to cost' here?

Yes, the verb maksaa means both 'to pay' and 'to cost'. You have to rely on the context to figure out which one it is. Since a book cannot pay for anything, it must mean 'costs' here.

How do we know it translates to 'The book' and not 'A book'?

Finnish does not have articles like 'a' or 'the'. The word kirja can mean either 'a book' or 'the book' depending on what makes the most sense in the context of the conversation.