How to flash official Android 4.3 Jelly Bean OTA Update for Samsung Galaxy S3 I9300

1. Download the Android 4.3 firmware update from here. (Vodafone Ireland Android 4.3 Update files).
   – if you want to download a different region build, then you can follow the SamMobile link here. Make sure to create an account in order to be able to visit SamMobile.
2. Extract the zip contents and place the “.tar.md5” file on your desktop.
   – don’t extract any further than that.
3. Download Odin from here.
   – extract Odin contents to a single folder.
4. Power off your Galaxy S3 now.
5. Boot the phone in Android Download Mode.
   – Press and hold Volume Down, Home and Power all at the same time, then release the buttons when the ‘Warning!’ screen appears. Press Volume Up to confirm the Download Mode boot.
   
6. Launch ODIN exe on your PC.
7. Connect your smartphone with your computer via USB Cable.
   – wait for Odin to recognize your Galaxy S3, then continue tot the next step.
   – if the phone is not added by Odin, then you need to switch between USB ports or re-install the USB Drivers.
8. Now, go to Odin screen, click on PDA and load the .tar.md5 firmware file.
   – don’t change any default settings and make sure that Re-Partition is disabled.
9. Click the START button whenever you’re ready for the updating process to begin.
   – don’t press any buttons until all files are installed successfully.
10. When the installation is complete, your Galaxy S3 will reboot and you can disconnect it from PC when the Samsung boot animation appears.
11. Enter your Google Account details. That should be all, the update to Android 4.3 is now complete.

These were all the steps you had to take in order to update your smartphone.
If the phone doesn’t boot in normal mode after installing all files, then you will be forced to apply a factory reset. This means that the data from system partition will be removed in the process, but the Galaxy S3 will be forced to boot in normal.
Here’s how to apply Factory Reset for your Galaxy S3 on Android 4.3:

• power off the device completely.
  – remove it battery, then re-insert it after a few seconds.
• boot your phone in Recovery Mode.
• select ‘wipe data/ factory reset’ and confirm.
• return to the main Recovery screen.
• reboot your phone in normal mode.
• enter the Google Account info and take control over your smartphone once again.

For any other questions or in case you cannot complete the tutorial, then you should ask for more help in comments.