is there an easy cheaper way?
As with many things, there's the easiest way and there's the cheapest way, and in most cases (especially for longer trips) they are not the same.
You have two broad options, unless you have something like Google Fi:
The first one is to keep your US number and SIM card and buy an international plan. This is generally the easier way. The pros are: no need to fiddle with SIM cards, you know what your phone number will be, friends/family back home have your number already. The cons are: it's generally more expensive than getting a local SIM card, especially if your trip is longer. If you're on Verizon, the only other reasonable option aside from the $10 per 24-hour Travel Pass plans is to buy one of their international data packages, but it's not a lot -- for $70/month you only get 500 MB of data. I can tell you that in a busy solo trip I can use up that much data in just two days.
If you keep your US number, you just dial other US telephone numbers as usual. To dial Italian phone numbers you would dial + 39 XXXX... where XXXX.... represents the Italian phone number. (The key isn't so much where the phones are located, as what the phone numbers are -- so if your friends are also using a US international plan, you should be able to call them directly as usual.)
The second one is to buy a local SIM card. This is generally the cheaper way. The pros are: it's generally a lot more cost-effective, especially if you are traveling longer or know you will use lots of data, and you get a local phone number, which means you can dial local businesses directly and give them a local number if they need it. The cons are: if you're buying in-country, you won't know what your number will be until you get there, and you'll have to let friends/family back home know your number (and they will probably have to use something like FaceTime or Whatsapp to contact you the most easily).
In this case, if you have an Italian SIM card, you dial Italian phone numbers "normally" (i.e. with no international prefixes) but you would need to dial US numbers in the format +1 555 555 5555, instead of just 555 555 5555 as you probably have it stored in your phone.
I prefer to do this, because I'm a heavy user of my phone. For example, I was recently in Germany and France for 11 days, and I had the Orange Holiday card, which for €40 ($45) gave me 20 GB of data, of which I used nearly 8 GB. There's no way any Verizon plan would have been as cost-efficient for me: using Travel Pass daily would have cost $110 ($10 for 11 days), so I saved $65 by using a local SIM card.
