Rooting the Galaxy Note is super easy with the Odin one-click rooting app. Here's what you need to know.
Step 3: Let's Get Started...
You'll need a Windows PC for this method, but other than that, it doesn't get any simpler. You'll just need to download a few files, boot up your Note in recovery mode, plug it into your computer, and run the Odin program. It'll flash ClockworkMod Recovery onto your phone, which you can then use to flash the necessary root files. For a full walkthrough, check out RootGalaxyNote.com's video rundown.
Then, when you're ready to see everything you can do with your rooted phone, check out Android Forums' All Things Root page for the Galaxy Note.
Step 4: For even more info, see: The Complete Guide To Rooting Any Android Phone