The telephone systems in both Chile and Argentina a very modern and relatively inexpensive. Public telephone offices can be found around all cities and even small towns. Most public call-phones accept coins and take cards purchased from bookstalls and newsagents. Some public call-phones also accept credit cards and some accept only coins. Per minute rates from public telephones to Europe and USA are around 50 cents (USD) per minute. Some places are higher, like to Australia.
Chilean and Argentinians widely use mobile phones. There is almost a complete coverage in cities and large towns but is in not reccomended as a reliable form of communication inside National Parks and for treks in areas far to the highways. Check with your phone company before leaving home about international mobile roam facilities available in Chile and Argentina.
Heavy and expensive, world phones allow you to make and receive call from anywhere. Satellite phones are about USD1.500 to buy or USD300 montly rent, plus from USD2 per minute to use. You also pay for incoming calls.
Access to Internet is not a problem except in "really out there" places like National Parks or in trekking trails. Internet cafés are common. Many public telephone offices offer Internet conection and broadband is also getting common by now. Rates are between 1 or 2 USD an hour and gets more expensive in remote areas. Tip: You can get the @ symbol by holding down the Alt key and typing 64 in spanish keyboards.
You will need a RJ45 type plug to be able to connect your laptop into a computer socket in Chile or Argentina and a Ethernet cable where broadband is available.