The best way to avoid roaming charges and other heightened fees for talk, text, and data overseas is to use a local SIM card at your destination. SIM cards give you access to a local phone number and the plans are usually pretty cheap, e.g. $10-$30 for 30 days.
Many people opt to use Wi-Fi while they are abroad. This is certainly an option to consider—especially if you're only going to be at your destination for a few days. But even for those few days, you may want to consider a local SIM card for some of the benefits it offers.
I used local SIM cards in most of the countries to which I traveled during my 15 month trip around the world. Along the way, I learned a lot about when it is and is not a good idea to get one and what to do to make life easier when setting up and using a SIM card abroad.