1) Install USB Drivers for Samsung Galaxy S3 on the computer.
2) Ensure that USB Debugging Mode enabled. [Press Menu>> Settings>> Applications. From there navigate and click on Development option and ensure the USB Debugging Mode is turned on.]
3) Create back-up for all the data of the phone. If the device is having any custom recovery installed, then make back-up for the same.
4) The phone should be factory unlocked.
5) Verify that the battery of Galaxy S3 should have more than 80 per cent of charge.
6) Rooting will the phone will void manufacturer's warranty.
Steps to root Galaxy S3 I9300 on Android 4.1.2 XXEMB5 Jelly Bean
1) Download CF-Auto-Root-SGS3-v6.4.zip for Galaxy S3 to the computer and extract the zip file
2) Download Odin v1.85 which will help to install the Jelly Bean firmware
3) Power off the Galaxy S3 and enter in to Download Mode. To do so press and hold the Volume Down, Home and Power buttons together until the construction Android robot and a triangle appears on the screen. Now press the Power button again to confirm to enter into Download Mode
4) Run Odin on the computer
5) Connect the Galaxy S3 to the computer using USB cable while it is in the Download Mode. If the phone is connected to the computer successfully, one of the ID:COM boxes will turn yellow with the COM port number. This step is likely to take some time
6) In Odin, click on PDA and select the CF-Auto-Root-SGS3-v6.4.tar file
7) Ensure the Auto Reboot and F.Reset Time options are selected in Odin
8) Double check everything and click the Start button in Odin to begin the installation which would take a few minutes to complete
9) Once the installation is completed, the phone will restart automatically. After the home screen appears, unplug the USB cable from the phone to disconnect it from the computer
Samsung Galaxy S3 I9300 running on official Android 4.1.2 XXEMB5 Jelly Bean is now rooted successfully. To ensure the root method is installed and is working properly, verify with the Root Checker