Italy is still rather old fashioned when it comes to paying for things. Cash is king! 

Some restaurants only accept cash, and those that take credit cards will usually prefer cash if you have it. Market stalls almost always trade only in cash, although a few have started to introduce credit card payment too. Gondole and taxis will mostly take only cash. In cafes, bars, tobacco shops, and similar it is unlikely that they will accept a card for small purchases. 

Cash machines can be found throughout the city. Some of them are inside banks rather than on the street.