You stamp the copy, never the card
An apostille is a single stamp one Hague country adds so another country takes a paper with no embassy step. It has to sit on a signature. Your card has none that Italy can check, so what you send is a certified copy: a sheet on which an officer writes that the copy matches what they saw. If you are asking how to apostille a Government-Issued ID Copy, that sheet is the thing being stamped.
Two signatures, two offices
First an officer certifies the copy. Then a second office stamps that officer's signature. Plain papers of this kind go to the Prefettura, the prefecture, which is the state's local arm. A copy done by a notary is a notarial act, so it goes to the Procura della Repubblica at the court. You can only apostille a Government-Issued ID Copy in Italy when an Italian officer made the certified copy.
The fee and the wait
The apostille cost for a Government-Issued ID Copy in Milan is a €16 tax stamp per document, and some papers are exempt, so ask before you pay. The office that certifies the copy may charge a fee of its own as well. Waits track the queue at the desk. To apostille a Government-Issued ID Copy in Milan in time for a bank date, allow spare days.
What it is for, and the language question
A stamped ID copy usually rides along with something else. Banks abroad ask for one to open an account, registers ask when you are named as a director, and notaries ask when they draw up a power of attorney for you. Check that the name and date lines match the other papers in the bundle, letter for letter.
The legalisation of a Government-Issued ID Copy in Milan finishes with the apostille when the reader's country is in the Hague group. Some desks also want the officer's wording in their own tongue, done as an asseverazione, which is a sworn translation that a court in Italy stamps. No one language is set here, so ask the reader to name it.