You can buy a SIM card (with an Italian phone number) in any mobile phone store or authorized dealer of the 4 major mobile phone providers in Italy:
TIM
VODAFONE
WIND
3 (tre)
They are ubiquitous and the shop assistants will install everything for you. In major cities the staff speaks English (and sometimes in small towns too, provided they are young. Most young Italians speak English to some degree).
The basic cost is €10 (with €5 of available voice/text). The SIM cards are rechargeable at any store (tobacconist or newstand) displaying the provider logo. Tobacconists can recharge them for you online, all they need is the phone number and the provider (e.g. Tim, Vodafone etc).
Data plans for smart phones are for a minimum of one month and cost more. The price for one month only ranges depending on the volume of data you need (expressed in Gigabytes). Vodafone 4G plan for 15Gb is €35. TIM's 4G for 10Gb is €30. That's way more than you will need for the time you go there. There are also cheaper plans for a lower amount of Gb and it's as low as under €10 for up to 1Gb.
All the info you need is here:
http://prepaidwithdata.wikia.com/wiki/Italy