To call Austalia from the United States:

011-CountryCode-AreaCode-PhoneNumber

Australian Country Code: 61

Area Code: Depends upon the State

In brackets are some major cities within that state.

• Australian Capital Territory (Canberra) - 2
  
• New South Wales (Sydney) - 2
  
• Northern Territory (Darwin/Alice Springs) - 8
  
• Queensland (Brisbane/Townsville/Cairns) - 7
  
• South Australia (Adelaide) - 8
  
• Tasmania (Hobart) - 3
  
• Western Australia ( Perth ) - 8
  
• Victoria (Melbourne) - 3
  

To call mobiles no area code is required, just chop the front "0" off the number and use the rest as the phone number.

A useful website:
Global Sources Travel Guide - Telephone info