For using your credit card in a foreign country, you will be charged a % on the exchange rate, plus possibly a flat rate fee per transaction. This will be hidden in the exchange rate so it may not be obvious.
Just to be clear, US credit cards will give you the interbank exchange rate at the time your transaction posts. Many cards do add a % foreign transaction fee onto that, but each card clearly spells out what that percentage is and typical is 3%. There should be no other credit card fees by either the bank or the merchant.
ATM cards will have the same interbank exchange rate but typically then a % foreign transaction fee and often also an out-of-network fee. The network fee is usually a flat rate of about $3-5 depending on your bank; the % is typically 1-3%.. Local European banks rarely charge fees. But do watch out for DCC (Dynamic Currency Conversion) which is becoming more common. It is an offer to convert your purchase or ATM withdrawal into US dollars for you, which means they get to set the exchange rate and typically pad it for their profit. You can ALWAYS decline it - someone telling you that you must accept it is scamming you (usually they will ask before but sometimes you'll see your price in US$ and that is your warning to say "wait a second...")
As noted, cash is king in Italy and many places that claim to accept credit cards may resist you actually using them. And merchants will be most unhappy, if not outright refuse to let you pay small purchases with one. Larger purchases at stores can almost always be done with a card. Oh and good luck making a small purchase with a large bill too. Always try and break those whenever you have the chance.