What's the smartest way to have access to your smartphone in Italy?

The first thing to do is to check your existing provider's roaming options on their website. They may provide an international or Europe-specific 'add-on' which offers you x amount of data, calls & texts for a set amount of money. For example, AT&T offer an 'international day pass' at a daily rate of 10USD. The daily charge is only activated if you use your phone in that specific 24-hour period.
If your phone is unlocked (i.e. isn't tied to a specific network provider such as AT&T) you can buy a pre-paid/pay as you go sim either online well before you go (to allow for delivery) or when you get to Italy, either at the airport on arrival (for example, there is a TIM shop within Rome Fiumicino airport) or when you arrive wherever you're based. You can buy sims from phone shops and also from many newsagents & 'tabacchi' (shops selling cigarettes etc). Prepaid sims are time-limited (often a month. sometimes 2 weeks) as well as data-limited.
Obviously sims vary in cost and coverage according to provider. Many Italian sim plans are, by law, only available to for residents so you'll need to look for sims available for visitors (they often have clues in the name e.g. 'tourist'/'viaggi'/'holiday').
Vodaphone, TIM and Windtre are the major Italian providers with the best coverage.
If your phone is locked to a provider you'll need to either a) get it unlocked (check provider's website). If you can't do that you'll need to buy a cheap, unlocked phone from e.g. Best Buy to take with you & put the Italian sim into. 
Remember to take at least one European plug adaptor with you!

Italy has lot's of little phone shops that sells local SIM cards. I think this will be the easiest and cheapest solution for you to use.