Sim card

Yes, that's correct but you must ensure that your phone is unlocked in order to use other SIM cards. The costs for calling the U.S., texting or using data (Apps and Google maps) will depend on which network carrier and the terms of whichever calling plan you choose when you buy the SIM.

We just got back from Italy. We purchased a Vodaphone holiday SIM at the foreign Exchange desk in Milan malpensa airport. I think it was €30 for 300 mins / 300 txt can (both of which can be used to Us/UK/Italy and others) plus 2GB of data.

Inserted it into an unlocked iPhone 4s a few hours after purchase (as instructed by the sales person) and it worked quite well.

Remember the PIN that comes w the SIM as my iPhone was temperamental and would shut down when the battery got below 20% and I needed to reenter the PIN after these crashes. Otherwise worked flawlessly.

And yes. All apps worked fine.

Is the unlocking of the iPhone reversible when you return home or did you use a different phone from your current one? I use an iPhone 5s, but still have my 4G. Though i don't like the idea of the extra weight, I'm a little concerned about screwing up my new phone.

Call your cell phone provider. They may not allow you to unlock a phone that is currently under contract (as it would free up said phone to be used by any provider).

I chose to use my old iPhone 4S since it was no longer being used as a phone (we upgraded a while ago) and Verizon unlocked all 4S's - so it was easier to just go that route.

You cell phone would likely rather you buy their crummy intl plan than unlock your phone. But good luck trying.

If your phone is fully paid, it can be unlocked (the company should give you a number to unlock it when you insert a different SIM card. If you bought it on your own, for ex at Apple Store, then the phone is unlocked already. Once unlocked you can switch SIM card back and forth at will.
If you decide to use your older iPhone in Italy and also take your new phone with you, it's very important that you disable the cellular data in your new phone, otherwise you will incur a lot of data charges while in Italy. Once you disable the cellular data (settings.cellular.cellular data off) your new phone will become a dumb phone. You will still be able to make or receive calls/texts but everything else is disabled. Use your old phone with the Italian sim for everything. Your phone with the American sim should be used only to receive important calls/texts on that American phone number (if you need to). Remember that even calls using your American phone cost at least $1 a minute while sending or receiving text costs about $0.50 each. So don't use it except for very important matters that can't wait. Your Italian SIM card with Vodafone for €30 will include 300 minutes and 300 texts that you can use worldwide. Use that one to call home.