As a resident of Italy, you are allowed to register
for national health insurance, called the mutua.
You do so through your local USSL
or ASL (Azienda Sanitaria Locale)
office. Once you are paying the mutua payments, you
can visit your assigned doctor, have exams done, and
get medications.
Foreigners who get national health insurance have booklets
(libretto sanitario) that only last as long as their
permesso di soggiorno. When applying, take your
passport, residence papers (both permesso di soggiorno
and residence certificate), and your codice fiscale
and proof of employment (dichiarazione del datore di
lavoro), or your marriage certificate.
A separate institution (INAIL covers all workers against the consequences of industrial accidents occurring in the course of employment.