How do I find a room, and how do I avoid scams?

Short answer: Apply for DSU or university housing, book a refundable short stay for the first month, then find a long term room with a proper contract. Never pay for a room you have not seen, at least by video, with a real contract.

Residences: cheapest but limited; usually applied for in summer with the DSU scholarship.
University housing office: ask for verified listings first.
Contracts: ask for a registered contract (contratto registrato). Italy has a special student contract, usually from 6 to 36 months. A deposit of one to three months' rent is common; get receipts.
Scam red flags: the owner is abroad and cannot show the room; money is asked for before viewing or contract; the price is far below average; you are pushed to pay today.

This page explains official rules in plain language. I am not an immigration adviser and I do not give visa advice. For that, always use official government sources. Rules change: confirm with your university, the embassy and VFS before you act.