1. Make sure your mobile should have 70 to 80% battery.
2. Enable USB debugging mode (Menu (app drawer) > Settings > Manage Applications > Development > USB Debugging – check box).
3. Ensure that you have backed up your all important data.
1. Download and install Samsung Galaxy S3 USB Drivers (Download USB drivers or download Samsung Kies (drivers included))
2. Download “Odin“.
3. Download “CWM Touch Recovery“.
4. Download “SuperSu“.
5. Download “Stock Recovery”
Install CWM Touch Recovery :
1. Download all files on your computer .
2. Extract “Odin.zip” on the desktop and place “CWM Touch Recovery for Samsung Galaxy Mega 5.8” in it.
3. Now boot your phone into Download Mode
4. Open “Odin.exe” (from extracted folder) and connect your phone via USB cable to your computer in download mode. If your phone is connected successfully the one of the ID:COM boxes will turn yellow/green.
5. Click on “PDA” button and select file “.tar.md5” (from extracted folder).
6. Now, click on the Start button on Odin to start the installation process.
7. when the installation process is completed successfully you will see the “PASS” message on Odin and then your device will reboot automatically. Now, you can disconnect your phone from computer.
((Finish You have successfully installed CWM Touch Recovery))
(Note: If in case CWM Recovery doesn’t work for your device then you can flash “Stock Recovery” via above method only, just by replacing “PDA” file.)
8. Place “SuperSU” file in external/internal memory of your device.
9. Now, boot in to recovery mode by pressing and holding “Volume Up + Home Button + Power Button“.
10. In recovery menu, choose “install zip from SD card” > Give a path to “SuperSu” file from an internal/external SD card > Give “Yes” to confirm to root Samsung Galaxy Mega 5.8.
11. When the installation process is completed select “++++Go Back++++” and then choose “reboot system” to reboot your phone.
FINISH now your phone is ROOTED