Your best value would be to get your iPhone 4S unlocked by Verizon so you could use a local SIM card once you get down to South America.
If you would not like to use a local SIM card, you can go HERE for an overview of Verizon's Global services and HERE to see what the cost would be for Verizon Global services while on you trip. For example, in Brazil, the cost/minute for calling would be~$2.00, $25/100MB of data allowance, $0.50 for texts sent and $0.05 for texts received. Using a local SIM card would most likely be MUCH less expensive.
You need to contact Verizon Global Services at 1-800-711-8300 if you would like to get your phone unlocked. Also, for an iPhone, after you insert the international SIM in your device, you will then see a prompt on the phone to connect to iTunes. You will not be able to use the phone until it is activated again thru iTunes on your computer or thru a WiFi connection.