Figuring out whether your phone will work on a different carrier is a pain in the neck for everyone. Finally, finally, someone has stepped up to fix it with WillMyPhoneWork.
The service, created by reddit user and presumed South Park fan ManBearCoon, will ask you a few questions about your phone including brand and model. Then, you'll choose a country and carrier you want to use it on and the site will tell you whether your device is technically compatible.
Of course, there are more factors to consider. Not the least of which is whether your phone is unlocked. The site also includes which bands are supported, but keep in mind that those still may be restricted to specific regions. However, this will get you a lot closer to the ballpark than random Googling. If the results say you've got a reasonable chance to expect your phone will work, call up your carrier and try to get it activated. Or slide a SIM in, where applicable.
You may find some issues with determining your phone's sub-model, since this isn't information that is always readily presented by manufacturers. While there's no one place that's guaranteed to show it, I found that going to any app on Google Play and expanding list of your devices that it's compatible with gave me the info I needed. WillMyPhoneWork also suggests checking Settings > About Phone > Model number (though this doesn't always have it). If you found yours somewhere else, let us know.
WillMyPhoneWork | via Reddit