It is one of the easiest yet.
Look up "odin root galaxy note 2"
That will tell you exactly how to get the phone rooted and a recovery flashed. The root is necessary to get the "authority" to make "unauthorized" changes and the recovery is so you can boot into a special "recovery" to flash your ROM.
The next step is to get a new ROM - make dang sure it is for your phone and carrier. You put it on your SD card and when you reboot into recovery you select flash rom, point it at the ROM on your SD card and let the magic happen.
I'm currently liking the CleanROM - it is only 4.1.2 but it keeps most all of teh TW goodness but has many customization features and runs the perseus kernel which has CPU and hardware tweaks PLUS it's tuned for superb battery life. I easy get a day and a half in normal use - up to 20 hrs with moderate use.
SlimBean is based on 4.2.2 so you get all the new goodies but I'm unsure if it supports the S-Pen and other extras.