Disclaimer: I am not responsible for any damage to your device while using this guide. It is always a risk to root your phone because of the nature of the process. Also this will void your warranty if you proceed.
Download the following files on to your desktop:
1. Open the Odin program on your computer by extracting the Odin named zip file and then double clicking on it. Also extract the rooting package to get the .tar file.
2. Turn off the device and once it is off press Volume Down (-), center button and power (in that order) and hold until you enter into Download mode. A green robot will appear on screen indicating that Download Mode has been enabled. If the device boots normally then you will have to try again as it did not work.
3. Now connect the Phone to the computer after which you will see that the ID : COM section will turn yellow. If this happens then all the necessary drivers have been installed successfully and you are ready to flash.
Note: If the ID : COM section doesn’t turn Yellow then install Samsung Kies if you haven't already done so and you're still having difficulties feel free to leave a comment at the bottom of this article and I will help you.
4. Next you will click on “PDA” and navigate to the “CF-Insecure-SGS3_XX_NEE_ALE8-v1.2.tar” file that you extracted in step 1 then click on “Start” to start the process of flashing your Galaxy S3 for root access. As soon as the flashing process is finished the device will be rebooted. Once you see the home screen you can disconnect the phone from computer.
Note: In case you are facing force close issues (this will wipe all user information on phone), turn off the GS3 and press Volume Up (+), Center button, and the Power Button (in that order) to enter into recovery mode. Once there you will select "Wipe data/factory reset" and when that is done wiping go further down and select "Wipe Cache" partition. Once that is done select "reboot system now". Now force closing should not be an issue anymore.
Congratulations, you have now successfully rooted your Samsung Galaxy S3 smartphone. If you face any issues as we will try to resolve them asap via the comments section below.