Most mobile phones sold in Australia are locked to the network that they were originally sold through (all phones sold by Telstra are locked), although a small number of phones are sold already unlocked. If your mobile phone is on a contract there is usually no problem getting your phone unlocked by simply calling your network and asking them to unlock it. Mobile phones on prepaid plans are usually locked to a network but if you have been with the same network for a while it can usually be unlocked by calling your mobile phone company. Pre-paid phones on Boost, Optus and Virgin Mobile can be unlocked after $80 of credit has been added to the phone.

Call 1300 555 002 to unlock a phone on the Optus network. If you have an iPhone on the Optus network you need to call 1300 075 395.
More information on unlocking phones on the Optus network
 
Visit a Telstra Store or call 125 8880 to unlock a phone on the Telstra network. If you have an iPhone on the Telstra network you need to call 1800 474 663.
 
Call 13 19 21 to unlock a phone on the Three network. NB: Three charge very high fees to unlock phones on their network.
 
Call 1300 650 410 to unlock a phone on the Vodafone network. There is a charge to unlock a Vodafone mobile.
 
Call 1300 555 100 to unlock a phone on the Virgin Mobile network
More information on unlocking Virgin Mobile phones

Please note that when you call your mobile network to unlock your phone you need to have the mobile you want to unlock with you and you need to call from a different phone to your mobile. You will most likely be asked for your phone’s IMEI number, which is usually printed under your phone’s battery.

It is more difficult if you are already in the United States, as many American mobile phone shops don't know how to unlock phones, especially phones on a foreign network. However there are several websites where you can generate codes to unlock your phone. These sites include Trycktill and Unlock it Free. If you are in the United States you can also try making an international call to your home mobile company to get an unlocking code, but occasionally you need to be calling from within that network's coverage area (depending on your mobile network at home).

You can read more about unlocking your mobile phone here.