This root method is for Windows computer, I will post another root method for Mac and Linux real soon.
To root using this method, you will need a Windows computer.
For Linux/Ubuntu, please see How to Root Galaxy Note 2 on Linux/Ubuntu!
For Mac OSX, please see How to Root Galaxy Note 2 on Mac/OSX!
Step 1. Put your Galaxy Note 2 into Download mode by turning off your phone first then holding down Volume Down, Center Home, and Power buttons together.
Step 2. Once you see the warning screen, hit Volume Up button to enter ODIN Download Mode then connect a micro-USB cable from your Note 2 to your computer.
Step 3. If you don’t have Samsung USB drivers installed, go ahead and download it below and run it to install.
Step 4. Next, download GalaxyNote2Root.zip