There are 3 major carriers in Argentina
Claro, Movistar and Personal
- All three offer prepaid cards you can buy on literally hundred of shops around the city (I am not sure were in Buenos Aires you are going, but if you are traveling to Capital Federal, then you will find shops on the streets, on every shopping mall, and big movie complex. There are some impromptu sidewalk shops across big avenues, but the discount you will get with them is not worth it).
- The first thing they will sell you is the chip(SIM) which is around $30 ($6 USD).
Once the number is activated, which is instantly, you can charge your new number on any kiosk around the city. You will see signs with a legend like ("Cargamos Personal/Movistar/Claro"). You will be asked for your number and the amount you want to charge and they will send you the credit instantly.You should receive an SMS confirmation with your new credit. You will have to pay with cash on most of the Kiosks. If you want to use a CC go to a branded store or use the online option at the official website for the carrier.
Personal Stores / Movistar Stores / Claro Stores
Make sure to ask the seller for current "deals". Quite often you will find 2x1 on all your credit (You will get $200 for $100) or unlimited SMS for 1 day, or free 500 SMS.
All three companies currently offer unlimited 3G for $1 peso a day ($0.20USD).
For Claro and Movistar (and probably Personal) you have free calls for clients of the same company.
Prices will vary A LOT depending on your plan. Make sure to ask the person selling you the chip which one is more convenient.
In Capital Federal is quite easy to find free WiFi. Almost every coffe shop, fast food chain or shopping mall will have open and free spots.
Finally if you are visiting Argentina with United States Dollars or Euros remember there is a huge differente between the official price and the paralel valuation.
$1USD can either be $4.90 pesos or $7.50 pesos depending which market you trade.
Hope it helps!