You need a 3 or 4 band GSM phone--I use cheap dumb phones-whatever ATT is giving away--but they have been GSM phones. (GSM is the cell phone technology used in most of the world.) With ATT I've never had to ask to have the phone enabled for international roaming--it just works. I just use it for emergency--last I looked 79 cents per minute in Canada--might be more in Europe. ATT will sell you an overseas plan which cuts the per minute charge in half-no great deal.
A warning--if you have friends visiting from Europe--if you call them on their cell phones, even if they're next door your cell company thinks they're still in Europe and you will pay international roaming.
Another warning--you can use your smart phone for data for free if you are in a wireless hot spot. If you're not and you get data over the 3G or 4G network you pay roaming. Worse--even if you aren't using the internet--if your smart phone is turned on it is connecting without you even knowing it--looking for updates and the like. Roaming charges. Turn it off.
Everyone under 50 already knows all this stuff.