There are 2 ways of doing that. Via Samsung Kies and OTA (over-the-air)
The OTA method:
Goto Settings --> About Phone --> Software Update --> Update. If you have Wifi then do so, or only GPRS, then uncheck the Wifi only option and update/download it.
The update file is around 36 MB, but if you haven't updated your Note for a while, you would get something higher than that.
As usual, it reboots a few times.
If there are no more updates available and you are still on the old version (with a few minor changes to the UI) continue with the Kies method.
The Kies method:
Download Kies from here.
And connect your phone. I din't succeed on Windows 8 CP. So I had to shift to Windows 7.
Update Kies. You will probably see that a new firmware version is available for you device. Click Update.
There is nothing much you will have to do. Just do not disturb the connections and if you have a slow or dodgy internet connection you will have a very hard time doing the upgrade.
You will find that your phone has Ice Cream Sandwich. ICS is just as smooth as Ice Cream. ICS is very much different from GB, which means, you'll just have to dig deeper.
I still haven't because I wanted to write about the success of upgrading after a war between me and my internet connection.
Let me know if you had any problems, because I had a few myself, I'd love to solve it along with you.