Just to be crystal clear: If you flash via Odin as I demonstrate in this guide there is no way to reset the flash counter. That means that your warranty is irreparably void, you cannot return the phone to a stock state for warrany purposes. You've been warned.
Only follow this guide if your Note already has no warranty and you'd prefer to use Odin because you are already familiar with it.
Your phone will flash a yellow triangle every time you boot it up to denote that the phone has been flashed unofficially. There's an app to remove it known as 'triangleaway'. Read the post here.
Even though the chances of going wrong are very few, but I am not responsible for any bricked device. Flash at your own risk!
Here is a list of things you will need:
A fully charged Galaxy Note
A micro USB connection cable
A Windows PC (I have no experience with doing this on a mac, so for now the guide will only cover Windows)
The PC will need to have the USB drivers for the Galaxy Note installed:
If you simply connect the Galaxy Note to the PC with the micro USB cable it will install them
To be very sure your device will be recognised by Odin connect twice - once with USB debugging enabled, and once without - different drivers are installed depending on the status of debugging (USB debugging is in Settings --> Applications --> Developement)
If you're still having no luck try also installing the latest version of Samsung's Kies
A copy of a program called Odin - you can download it here
The correct CFRoot kernel from here
Alright, now we've got all those things assembled, it's time to void your warranty! Here are the steps you need to follow:
Click the button "PDA", shown in the picture below. Navigate to the CFRoot kernel you downloaded earlier and select it.
Make sure "Repartition" is NOT checked.
Power down your phone, and then put your phone into download mode. Do this by simultaneously pressing and holding the Volume Down and Home buttons, and then while holding these buttons down press and hold the power button down until something appears on the screen.
Follow the instructions on that screen and press the Volume Up key to proceed into download mode.
Connect your phone to your computer with the USB cable, after a few moments Odin should recognise the device.
In Odin press the Start button.
Odin will flash the kernel to your device.
Your device will reboot, disconnect the device
Congratulations, your Galaxy Note is now Rooted! You should now make a Nandroid backup of the ROM using the Clockworkmod app that pops up in your app drawer.
Credit: Chainfire at XDA - please donate to him to keep his amazing Android development efforts alive!