Samsung Galaxy SIII GT-i9300 Android 4.1.2 update :

1. Download Samsung KIES  from : Here  and install the proper drivers for your Samsung Galaxy S3 device, if you already have installed the compatible drivers, you can skip this step.
2. Download the ODIN app from : Here and install it in your PC
3. Download the Official Jelly Bean 4.1.2 OS update file from : Here and extract the same in your PC.
4. Open ODIN application from your computer.
5. Power off your S3 device and reboot the same into Download Mode, to do this reboot the device by pressing and keeping the Power and Volume buttons simultaneous.
6. Connect your S3 device to the PC using the USB cable for doing that.
7. In the ODIN app,  you need to be notified with the ID:COM yellow or blue and the  “added” message is displayed and available. That’s give you the accord to begin the flashing process. If not, close ODIN, after that disconnect your S3 device from the computer and reinstall the drivers again in your PC after you reinstall the drivers repeat the procedure from the beginning.
8. Now, from the ODIN app select the “PDA” option.
9. Search and pick the downloaded update which you downloaded and extracted previously.
10. Now, in the ODIN app click on “Start” button.
11. Now wait until the flashing process is done and you’re notified by a “pass” message in the ODIN app interface.
12. Disconnect your S3 device by removing the USB cable.
13. Reboot your Samsung S3 device.
14. An Android Icon will appear on the device , it means that android is Updating

Screenshots :