Yes, a local SIM card would be the best choice. Make sure your phone is unlocked so you can do the switch and that it is tri/quad band so it works on Italy's networks.
For the SIM card, all you need to do is walk into any of the stores for the carriers here in Italy - the main ones are TIM, VODAFONE, WIND and 3. They offer prepaid SIM cards, generally the minimum requested is around 10 euros for the card which comes with some credit for minutes. It varies depending on the carrier.
You will need to show ID such as passport, since each card is registered nationally to a person.
If you're going to stay in main towns, 3 and Vodafone are pretty economical.
If you're in the countryside as well, TIM tends to get better coverage and also has good rates.
Ok this is just some of the most basic info, if you need more precise details, I's suggest searching and looking at the websites of the main carriers, as the offers change often.