As the Galaxy Note 10.1 is still a relatively new device, there does not seem to be so much help or development around. I stumbled upon this method of updating my Stock rom and thought it was worth contributing. The information is already distributed around the forums, but not specifically here for the Galaxy Note 10.1.
Please note you follow this guide at your own risk, I am not responsible if you mess up your tablet
1. Your starting point should be a rooted rom on your tablet. This is required for Mobile ODIN Pro to work. If you have not done this, then this thread should be followed first.
2. Download Mobile ODIN Pro from the Playstore. This has the advantage over the Lite version in that it can root a stock rom as you flash it. For more infomation on how to use this app see this thread.
3. Find your rom on sammobile. You will also need to register with the site in order to download the rom. Please note the roms for the Galaxy Note 10.1 are large - approaching 1GB!
4. Once downloaded, you need to extract the .tar file from the .zip and transfer it to your tablet.
5. Fire up Mobile ODIN Pro, grant superuser permissions. Select Open File and navigate to the .tar file you transferred. This will assign the relevant parts of the rom to the different partitions.
6. If you have flashed CWM recovery you need to go to the Recovery partition file and clear this otherwise you will get the Stock recovery again.
7. The key advantage of Mobile ODIN Pro is that you can inject root files as you flash the rom. So under EverRoot select Inject Superuser and Inject Mobile ODIN.
8. Set the Wipe data and cache and Wipe Dalvik cache settings to your choice. I left them unticked and therefore did not loose any data or apps I had already setup/installed.
9. Flash the firmware and enjoy
Specific thanks to Chainfire and zedomax and the SamMobile website