Not exactly sure where you got that information.
Bancomat is just the Italian term for ATM machine, it's not a specific institution. Every bank office will have a Bancomat machine, just like all banks in America have ATM machines. When you see the sign Bancomat it means ATM. Use it just like you would use it at home. However you need to call your bank before going overseas and tell them you will use the card abroad, otherwise they'll think it is a fraudulent use and will block it.
You will get the best exchange rates from the ATM (bancomat in Italian), much better than AmEx offices or the Exchange Bureaus scattered all over major tourist cities. However your American bank will probably charge you a flat fee for using the card abroad. Chase bank for example charges me $5 ATM fee for each ATM withdrawal overseas (I don't use it anymore, since I have an Italian bank account). So inquire with your bank. If your bank charges a hefty fee (like Chase), it is advisable that you make few large withdrawals rather than many small ones, because whether the withdrawal is just 50 euro or 500 euro, the fee your bank will charge you is the same.
Credit cards will also give you good exchange rates (however some charge a 3% foreign transaction fee). Therefore using the credit card to make payments is a good idea, at least for large purchases. Consider however that Italian merchants often give you a discount on the price if you pay cash (credit cards charge merchants a commission), so don't be afraid to ask if they give you a discount for a cash payment.
Also with Credit cards you need to contact your credit card before traveling abroad, to alert them you will be using the card overseas, otherwise they'll block it for fear of fraudulent use.
Bancomat machines are everywhere there is a bank branch, so basically everywhere. Italy has the largest concentration of bank branches in the EU. If you are in any town over 2000 people there will be at least one. In Venice and other large cities there are plenty more.