Step 2: Download ODIN 1.85, which we’ll be using to flash the insecure kernel.
Step 3: Once you’ve download both, extract using the archiving tool of your choice. I use WinRar, but if you’ve done this before, you’ll probably have your utility of choice already installed.
Step 4: After extracting the kernel, you’ll be left with a .tar file.
Step 5: Place your device into Download Mode by pressing and holding the Volume Down + Power / Lock buttons simultaneously, and pressing Volume Up when prompted.
Step 6: Run ODIN, connect your device to your PC via USB, and within ODIN, click on PDA and select the .tar file you extracted from the insecure kernel.
Step 7: Click Start and the flashing process will begin.
Step 8: Now you will need to "upgrade," as it were, from insecure to full root. To do this, you’ll need to boot your Galaxy S III, and enable USB Debugging by browsing to Settings > Applications > Development.
Step 9: Your insecure root allows adb root commands, but won’t enable your apps to get superuser access; thus, you’ll need to install SuperSU.
Step 10: Download the sgs3-root-install.zip file [XDA Developers link], which contains SuperSU v0.89, and extract it.
Step 11: With adb running, double-click the install.bat, and after a reboot, your Samsung Galaxy S III will be fully rooted!