Learn Italian: Ci sono volute due settimane per trovare un nuovo istruttore. - It took two weeks to find a new instructor.

The verb is volerci (to take time). In the past tense, it uses the auxiliary essere, meaning the past participle must agree with the subject. Here, the subject that "took" the time is due settimane (two weeks), which is feminine plural, so we use sono volute.

Could I use metterci for this sentence instead?

Yes, but the grammar changes! If you wanted to say "I took two weeks", you would use metterci with the auxiliary avere: Ci ho messo due settimane. Because it uses avere, the past participle messo does not change to match the weeks.

Why do we need the word per before trovare?

When connecting the time it takes with the action being done, Italian uses per. You can think of it literally as "Two weeks were needed in order to find a new instructor."

Why does the adjective nuovo come before the noun istruttore?

Nuovo is one of the common adjectives that often sit before the noun. Placed before, it usually means "new to us" or "a replacement" (another instructor). If placed after (un istruttore nuovo), it would emphasize that the person is brand new to the job.