European Union nationals in possession of an identity document are free to stay in Italy or other European countries for up to 90 days without any formalities.
Non-European Union nationals who stay in Italy for a maximum of 90 days (e.g. visitors, students, tourists, or on business) do not need a residence permit.
They do need, however, to present a Dichiarazione di presenza (Declaration of Presence) at police headquarters (Questura) within 8 days of arrival. This is not necessary under one of the following conditions, i.e. when:
an Italian stamp was put on their passport on entry into a Schengen area from an Italian border;
they are staying in hotels, B&Bs, university accommodation or student residences.
This declaration of short-term presence in Italy does not entitle you to work and cannot be converted into a work permit. You should always carry it with you in case of police checks.
SAOS - Servizio Accoglienza Ospiti Stranieri (Immigration Support Service)