Buy an International SIM Card
Although it requires planning and the right kind of phone, buying a SIM card is one of the more hassle-free approaches to making and receiving calls while overseas. Instead of renting or buying an entire phone that's local to wherever you're headed, you can order a dedicated SIM card and slot the tiny chip into your existing handset. Rates vary based on provider and whether you choose a multi-country international sim, or one that's specific to a region or country, but Telestial's $29 Explorer SIM comes with $10 of calling credit, with rates starting at $0.20 per minute for calls, and $0.35 per MB for data.
To note: Only models that connect via GSM will work in most non-U.S. mobile networks, and they must be unlocked. You'll want to confirm both details with your carrier.