Learn Italian: L'hotel è al completo: non ci sono camere libere. - The hotel is fully booked: there are no free rooms.

In Italian, the letter h is always silent. Because the spoken word starts with a vowel sound, it takes the article l' just like native Italian words that start with a vowel (for example, l'orologio).

Why use the phrase al completo instead of just saying the hotel is pieno (full)?

While you could say l'hotel è pieno, the phrase al completo is the standard, natural way to say fully booked or at full capacity for places like hotels, restaurants, and theaters.

Does libere mean free as in costing no money?

No, here libere (the plural feminine form of libero) means free as in available or unoccupied. If you wanted to say the rooms cost no money, you would use the word gratis.

Why do we use ci sono in this sentence?

Ci sono translates to there are. Because camere (rooms) is plural, we must use ci sono instead of the singular c'è (there is). To make it negative, you simply put non directly in front.