There are 2 methods I will describe for you here.
First Method is easiest, as it uses an App from the Google Play Store
Second method uses Windows 7, some software and your USB cable to unlock your Galaxy S3
For both methods, your Samsung Galaxy S3 should already be rooted.
These tools are used at your own risk - I will not be held responsible for any damage caused to your device by using these tools.
On your phone, go to the Google Play market and download Voodoo Galaxy S III SIM Unlock.
Follow the simple instructions from within the app and within seconds you will have unlocked your Samsung Galaxy S3 for Free !
To start, download Valhalla Unlocker - Galaxy S III from here
Extract the files to a folder on your desktop
Connect your Galaxy S3 to your PC with the USB cable
Run the program: Valhalla Unlocker - Galaxy S III.exe
Refresh to find your phone, then choose your phone from the list.
Click on Unlock My Phone
The above screen should load.
Click step 1 - allow this to complete
Click step 2 - allow this to complete
Click step 3 - allow this to complete
Click step 4 - allow this to complete
Congratulations - Your Samsung Galaxy S3 Is now Unlocked to use on any network with any simcard.
Information from the developer:
It automatically backups your original files to a folder called backups, in the same location as the extracted Valhalla files are placed.
After completing the 4 steps for unlocking, you should have an fully SIM-unlocked Samsung Galaxy S III (GT-I9300 ).
It can take up to 15 seconds after completing the unlock for your phone to connect to your service provider's network.
You may also notice that phone .apk crashes a couple of times during the unlocking process, it is completely normal, just press OK and continue.
Future versions will include the ability to re-lock your phone from backups made by Valhalla or Voodoo Galaxy S III SIM Unlock.
Thanks goes to 'oxterc' from XDA forums for this tool.