You need to make sure your phone is tri-band (or quad - most modern ones are but you never know) and is "unlocked" before you travel. This permits you to change out the SIM card inside and use it here with a local prepaid SIM card. TIM is the main carrier which I suggest you use since it has the most coverage no matter where you are (have learned this the hard way).
You go into any TIM shop once you arrive (they are everywhere), they make a copy of your passport and for 10 euros you walk out with a new prepaid SIM card with 5 euros credit to use while you're here for calls within Italy. You can add more cash to the car at most tabacchi shops or even through bank ATMs.
If you download and install Skype on your phone before you come, once you're here take advantage of all the free Wi-Fi areas (within where you're staying, for example, or even around coffee shops or in towns - for example, Florence's main squares all have free Wi-Fi) and use the Wi-Fi connection to make calls back home. You can also buy minutes on Skype to call landlines in the US, so you don't necessarily need to have the other person you're calling have Skype installed on their computer or phone. I think that's the best solution while you're here!