The citizens of the European Union can stay in our country for up to three months without any conditions or formalities, provided they possess a valid identity document for travel issued by their own country.
If their stay lasts longer than 3 months but less than 12 months they must register as temporary residents at the registry office (ufficio dell’Anagrafe) of the town of residence.
The registration must be requested directly from the concerned person, who can also present the request for his/her family unit.
You will not receive any certification about your registration, ONLY the European citizens will receive this document, due to regulatory obligations.
The registration has the validity of one year maximum, then the Anagrafe provides for the automatic cancellation from the list.
When the stay exceeds 12 months, the citizen can no longer be considered temporary and must therefore apply for registration in the register of resident population (additional info here)
Additional info and Anagrafe contacts can be found here