Which version of the rules?
Bylaws change. A meeting votes an amendment, the notary writes it up, and the old text is dead. So the first question is which version the reader wants: the text as it stands today, or the one in force on a past date. Ask them plainly, because ordering the wrong sheet wastes the whole chain. That is really where how to legalize Company Bylaws begins.
Who gives you a copy you can use
The notary who wrote the last amendment holds the file and issues a certified copy of the current text. A company registry extract is a different animal and will not stand in for it. Say out loud that the copy is going abroad, so the clerk seals and joins every sheet. You can then legalize Company Bylaws in Florence with a copy the next desk will accept.
Why the court stamps it, not the Prefettura
Rules drawn up before a notary are a notarial act. That sends them to the Procura della Repubblica at the court in whose district the notary works. The Prefettura is the state's provincial office and it handles administrative papers from town halls. The split is fixed by what made the paper, never by what the paper is about. The consular legalization of Company Bylaws in Italy follows that same split.
Fees and days
A €16 marca da bollo covers the state stamp, and you buy it before you queue. The mission of the receiving country then charges what it likes, and company files sometimes cost more than personal ones. Budget 10–15 business days, or 3–5 on the express route. The embassy legalization of Company Bylaws in Florence is where most of the wait sits, so ask for its diary early.
How the far end reads it
A bank abroad reads the rules to see who may sign for the company and up to what limit. A registry reads them to check the share structure before it lets you open a branch. Point the reader at the clause they need, because a long text invites long questions. An embassy attestation of Company Bylaws in Florence proves the paper is genuine, not that a clause means what you say.