Learn Polish: Ona czyta piętnastą książkę. - She is reading the fifteenth book.

Ordinal numbers act like adjectives in Polish, meaning they must match the noun they describe in gender, number, and case. Because the book is the direct object of the verb czyta, it takes the accusative case. The basic feminine form piętnasta changes its ending to -ą to become piętnastą, perfectly matching the accusative feminine noun książkę.

How do you form the word for "fifteenth" from the normal number 15?

The standard number fifteen is piętnaście. To turn teens like this into ordinal numbers, you drop the -cie at the end and add standard adjective endings. So, piętnaście becomes the masculine piętnasty, the feminine piętnasta, or the neuter piętnaste.

Just to refresh, why is the word for book spelled książkę instead of książka?

The book is the direct object of the sentence because it is the thing being read. This requires the accusative case. For feminine nouns that end in -a in their basic dictionary form, the ending changes to -ę in the accusative case.

Is the word order strict? Could I say: Ona czyta książkę piętnastą?

It is best to stick to the order shown here. In Polish, ordinal numbers generally go right before the noun they describe, just like in English. Putting the number after the noun sounds like a very formal catalog list or puts a heavy, unnatural emphasis on the number.