If you plan on using your smartphone when traveling overseas, it may be worth checking to see if your phone is compatible with the wireless bands in that area.
First, you'll need to make sure your phone uses the right kind of wireless technology -- CDMA or GSM. In the United States, Verizon and Sprint use CDMA, but AT&T and T-Mobile use GSM. GSM is the more widely used type of network around the world, so if you're on Verizon and Sprint, you'll want to first make sure your phone also can operate on a GSM network. The iPhone 5 and up can work on both types of networks, but you may need to have your carrier unlock the phone first.
Second, you'll have to check to see if your phone can operate on the wireless bands and frequencies used in the country you're traveling to. This can get a little more complicated, though. Fortunately, there are a couple of websites that will help you quickly find out where in the world your phone will work.
GSMArena.com has a section of its website that allows you to select the country you're interested in, and find phones that will work in that region. Another site that makes this process simple is willmyphonework.net. Just enter the brand/model of your phone and select a country.
Once you find out whether or not your phone will work, you can find an affordable data plan in that location at prepaidwithdata.wikia.com.