I use TripCase to organize my travel on my smartphone, and they partner with OneSim. If you use the link on the TripCase app to go to the Onesim website, you get $10 off your purchase. I bought a simcard that fit into my iPhone 5s. Remember to call your carrier in the US to unlock your phone for use with a third party simcard. Because my carrier only allows this abroad, I wasn't sure my card would work once overseas. But I followed their instructions (you might go to the store if you're not comfortable restoring your phone from a backup on your own), and it worked fine. I kept my phone in airplane mode the entire trip, used wifi, and made exactly one call to confirm an arrival time with a hotel.
In retrospect, I think it might have been cheaper and easier to buy a prepaid phone in Europe, but this was convenient as well for the amount that it got used.