- Make sure you have installed the updated Samsung drivers here (There is usually just one driver for all Samsung devices, but you need the updated ones that support the Galaxy S3)
- Download Odin here (Odin is a program that will push the modified recovery software to your phone)
- Download ClockworkMod Recovery here (custom recovery software that will allow you to give you root access and put a custom version of Android on it)
- Download the Superuser app for Android here
- Unzip Odin and double click the Odin3 v3.04 file
- Put the superuser zip in the root of the sd card
- Turn off your phone
- Once the phone is off, HOLD Volume Up + Home Button + Power Button until you see a warning that you are in download mode. Press Volume Up to continue.
- Plug phone into computer via USB; You should see a message in Odin on the left lower corner saying Added
- Uncheck the Auto Reboot and F. Reset Time
- Click PDA and find the downloaded Recovery .tar file
- Click Start.
- After it says Successful, unplug the phone and take out the battery.
- Put battery back in, and then HOLD Volume Down + Home Button + Power Button until you see some blue letters on the top of the phone screen.
- Now use the volume buttons to select install zip from sd card, then press the power button to select it
- now find the superuser zip and select it, and then confirm it
- now go back to the main screen of the recovery software and reboot
That should do it. Cheers.