The system update process to Jelly Bean (Android 4.1.1, 4.1.2 and 4.3) is fairly straight forward and depending on your network speed can be completed in under half an hour.
Caution: Before upgrading your phone it is always recommended that you backup your data.
To update your Galaxy S3 phone to Android 4.1.1, 4.1.2 and 4.3:
- Click on the “Menu” (left) button and Select “Settings” from the popup menu
- Click on “Application Manager”
- Select the “All” view to see all running applications
- Click on “Google Services Framework”
- Click the “Clear Data” button
- Click the “Force Stop” button
- Open “Menu>Settings” again
- Click on the “System Update” option
- Click on the “Update Samsung Software”
BAAM it’s done! In a little under a half hour you will have the 348MB (4.1.1)/157.6MB (4.1.2)/~500MB (4.3) download and it will automatically install after a reboot.
Disclaimer: Use at your own risk.