1. Connect your phone to the computer with original USB cable.

2. Copy downloaded ROM and Google Apps zip files to the root folder of your phone's SD card. Important: Do not extract any files.

3. Disconnect USB cable from the computer and power off your phone.

4. Boot into recovery mode. To do so, press and hold Volume Up, Home and Power buttons together until the screen flashes, and then release all buttons. NOTE: Use volume buttons to scroll and Power button to select an option in recovery.

5. Take a Nandroid backup of your current ROM so that it can restored later if something goes wrong with the new ROM. To do a backup, choose Backup and Restore and then hit Backup again on next screen. Return to main recovery menu once backup is done.

6. Perform a full data wipe process. To do so, choose Wipe data/factory reset, then hit Yes on next screen to confirm. Wait for a few minutes until the data wipe process completes.

7. Choose

8. Once ROM is installed, repeat step 7 but choose GApps file instead of ROM to install Google apps package.

9. When Google Apps is installed, return to main recovery menu and tap Reboot System Now to reboot the phone into Android 4.2.1 Jelly Bean based CM10.1 ROM. The first boot may take about 5 minutes. So, leave it alone.

10. Restoring Previous ROM: To restore your previous ROM, boot into recovery, choose Backup and Restore then restore your previous ROM by selecting it from the list.

Android 4.2.1 Jelly Bean based official CM10.1 ROM is now installed and running on your Samsung Galaxy S3 I9300. Go to Settings > About phone to verify the firmware version installed.