When I moved to Switzerland I wan able to asily buy one, without alot of paperwork, I went in with my passport (which is required) told them I wanted a SIM card, gave them my local address, and 50CHF later I had a local SIM. I'm sure this processis no different in Italy.

As for Italian providers, my Swiss phone usually switches to T-Mobile when I cross the border. I'm sure there are many other providers and walking around the city wil yeild tons of shops. All she has to do is pick one. The school she is studying at should be able to provide some information on it.