If you have not updated to 4.3, go here.
If you have not updated to 4.4, go here.
Finally, there is no guarantee that either method will work for you.
Root Method #1:
The first thing you should try is CF-Autoroot since this has worked for many users.
If you successfully root with this method, you can simply install Goo Manager or ROM Manager and install recovery.
This method failed for me after many attempts.
Here is some potentially useful info for root method #1 from ansonantonym.
Root Method #2:
1) Reboot in to download mode
2) Flash TWRP with Odin via PDA
3) Reboot to recovery then flash SuperSu and the Knox Remover
5) Download SuperSu from the Play Store
6) Open SuperSu and update the binary when prompted
8) Enjoy rooted 4.3/4/4
TWRP (Odin flashable tar)
If you found another method that worked for you, please post here so that others may benefit.
If you are uncertain about any of the steps above, please ask your questions here before proceeding.
Please be sure to thank Chainfire, Dees_Troy, and Kaito95.