On Androids, once you're in the other country go to 'settings', then 'battery & data manager'. Turn off all data and background data. Then in 'wireless & networks' turn on 'automatic' for network if you have a global phone. Some phones, especially if you are with Sprint, won't work outside the USA. Also, at least with Sprint, you have to call customer service before you leave home and tell them to activate worldwide service, otherwise the foreign networks won't recognize your phone.
There is a charge for texts on Sprint too, 5 cents incoming and 50 cents outgoing. For data, I just use Wi-Fi. Unless you answer a phone call or make one yourself, there isn't a charge for being hooked up to the network.
I just came back from a three-week vacation in Australia, and the phone worked perfectly the whole time. I could choose which calls to answer or texts to send, and used Wi-Fi for data. I also use that for Skype to talk to family & friends back home instead of racking up data charges. Piece of cake.
HAL