1. First of all make sure that you installed USB drivers for Samsung Galaxy Note 2 on your Computer. If not, then you can download and install the same from here.
2. Your device must have minimum 80% battery charge.
Hey friend, please remember one thing, you are updating your device at your own risk, and we are not responsible to you if your device is hanged or getting any problems.
How to Root Samsung Galaxy Note 2
STEP 1) Download the Firmware from Here and extract the file on your computer.
STEP 2) Now Download Odin3_v3.04.zip and extract it to your desktop.
STEP 3) Next turn on USB Debugging from Settings > Applications > Development > USB debugging options.
STEP 4) Turn off your Galaxy Note 2 and boot it into Download/Odin Mode: press and hold Volume Down and Home (center) keys simultaneously
and then long press the Power key till you see a screen that prompts you to press the Volume Up key to continue.
STEP 5) Press the Volume Up key to enter the Download Mode.
STEP 6) Now open the Odin folder and run the .exe file present there.
STEP 7) Connect your Galaxy Note 2 with the Computer via USB data cable while Odin is open
STEP 8) Make sure that only F. Reset Time and Auto Reboot boxes are checked on Odin. Do NOT check any other item.
STEP 9) Now click on the PDA button and select the CF-Auto-Root-t03g-t03gxx-gtn7100.zip.tar file.
STEP 10) Then, click on Start button to start the installation process and this process will take around 6-7 minutes to complete
STEP 11) Finally, you will see a PASS! message on the ID:COM box and then the device will reboot automatically.