The sheet that travels, and the one that stays
Becoming an Italian citizen leaves you with a decree and an oath sworn at a town hall. The town hall then holds your citizenship in its register, and it can print a signed sheet that says so. That sheet is what usually travels. If you are asking how to apostille a Certificate of Naturalization, it is the sheet you take to the desk, not the decree.
An apostille is a single stamp one Hague country adds so another country takes the paper with no embassy step. It sits on the signature of the officer who signed your sheet. A page printed off a portal, with no signature on it, gives the desk nothing to work with.
The office that stamps it
Plain civil sheets go to the Prefettura, the prefecture, which is the state's local office. Sworn and notarial papers go to the Procura della Repubblica at the court, so this errand stays on the plain side. You can only apostille a Certificate of Naturalization in Italy when an Italian office issued the sheet. A paper from another state has to be stamped there.
Fee, and how to plan it
The apostille cost for a Certificate of Naturalization in Milan is a €16 tax stamp per document, with some papers exempt, so ask before you pay. If you send the sheet and a copy of the decree, that counts as two documents. Waits move with the queue, so leave slack. To apostille a Certificate of Naturalization in Milan for a consular date, start weeks ahead.
What readers do with it
Consulates ask for a stamped citizenship sheet when you register a birth, claim a passport or bring family over. Employers and vetting desks ask when a post is closed to non-citizens. Pension and tax offices ask when a treaty turns on which country you belong to. Send the sheet with whatever else they listed, in one bundle.
The legalisation of a Certificate of Naturalization in Milan finishes with the apostille when the reader's country is in the Hague group. Many desks then want the text in their own tongue as an asseverazione, a sworn translation that a court in Italy stamps. Your birth name may be spelled another way there, so flag any gap yourself.