You can get an application from the ARRL. It just asks basic information that you send to:
Radio Club Argentino
Carlos Calvo 1424
1102 Buenos Aires
The club is the national amateur radio society in Argentina, and it mediates between the applicant and the administration for smooth issuance of a permit. My stay in Argentina was a last minute addition to my trip so I didn't apply until the 4th of August. The permit was dated 5 September and my office had it shortly thereafter. As I was already on my trip at this point I had my office fax a copy to me.