Calling Argentina from the United States explained:

• 011 - US exit code; dial first for international calls made from the USA or Canada
• 54 - Country Code for Argentina
• Phone Number (may not begin with 0) - 10 digits for both landlines and cell phones, area code included
• sample call from US to a landline in Buenos Aires: 011 54 11 ???? ????

How to dial to Argentina cellular:

• add digit 9 (nine) between the country code (54) and the area code of the city you are calling; you will have 011 + 54 + 9 + ten digits.
• if the cell number begins with 15 you must drop these two digits and add the area code instead
• example #1: you want to dial a cell phone in Bahia Blanca; this is what you will dial from the US: 011 54 9 291 ??? ????
• example #2: someone from Buenos Aires gives you a cell number of the format 15 ???? ????; you will replace 15 with the area code of Buenos Aires (11) and dial the following: 011 54 9 11 ???? ????

Area Codes:

Phone Books:

• Paginas Amarillas - several directories for business and people searches (in Spanish)
• Telexplorer - reverse search by number (in Spanish)

Updates:

• Argentina telephone numbering changes - November 2011 - April 2012