The first and most important thing to figure out is whether or not you actually own your phone. Most people don't realize that when you sign up for a contract and get a special price on a new phone, you don't own it. The carrier does. It's almost like leasing a car.
If you don't own the phone, your options are limited. You may be able to get a temporary international plan from your carrier or you'll need to use a different phone for your trip.
If you own the phone and bring your own device (BYOD), or if you have an unlocked phone, you may be able to use an international prepaid SIM card while traveling. If you own your phone in the U.S., your carrier is required by the FCC to unlock it for you.