So you just bought the Samsung Galaxy Note 3 Neo and now you want to root it. We finally have the steps on how to do it quickly. For now they only work on the SM-N7505 model which is the LTE model.
We have the instructions on how to root the Samsung Galaxy Note 3 Neo N7505 using CF-auto root method.
First you need to make sure that you are running the official Jelly bean 4.3 ROM for N7505. If you are unsure then download it from here. Steps for flashing it are given in that post. Also you should have a custom recovery something like TWRP or CWM should just do the job well.
Then download the CF-auto root from here and flash it by following these instructions.
Flash the CF-Auto-Root package as PDA in ODIN, and your device should reboot into a modified recovery and it will install SuperSU for you and restore the stock recovery, and reboot back into Android.