OK, so I'm going to give downloads and preparation first, then the instructions.
Downloads:
You need the latest TWRP -
http://dl.twrp.me/m8/twrp-2.8.6.0-m8.img
You need the latest version of SuperSU, copied to your phone from your PC, and you must install it from TWRP -
http://download.chainfire.eu/696/SuperSU/UPDATE-SuperSU-v2.46.zip
Preparations:
If you don't check md5 checksums first before installing anything, you'll regret it (excellent way to brick a phone).
Check out "AFV File Verifier for Android™"
https://play.google.com/store/apps/details?id=sa.afvx
Use that to check SuperSU from your running phone.
The target values you want are on the download sites for both TWRP and the SuperSU.
To check the TWRP image you need the tool for that, we include it in the Mini-SDK, the sdk-tools.zip file and instructions for use are here. You don't need any special drivers.
http://androidforums.com/threads/adb-guide-updated-2014-11-11.443072/#post-5389081
Unzip the sdk-tools.zip file, it produces the sdk-tools folder
Place the TWRP download there. (If you already have your own tools and don't choose our Mini-SDK, move the TWRP file over to wherever your fastboot is.)
Windows Explorer, shift+right click the sdk-tools folder, choose open command window here.
In it say -
md5sums twrp-2.8.6.0-m8.img
To copy and paste commands from here -
Alt+space in command window, E for edit - the paste option appears.
The return value you want is -
4970007ee43d536c5e64b56d6b4557b8
Download again if not matching.
Copy the SuperSU zip file to your storage via Windows Explorer. Check the md5 checksum value when done against the one from the download site using AFV.
Instructions for use:
Power down. Hold volume down while powering on, bootloader appears. If it doesn't say FASTBOOT at the top, tap power as instructed on screen so it enters FASTBOOT mode - plug in to PC, it will say FASTBOOT USB.
If you skipped the md5sums step (not a good idea), then now open Windows Explorer, shift+right click on the folder where fastboot is. If you used our Mini-SDK then you want the sdk-tools folder. Shift+right click on the folder, choose Open command window here.
In command window -
fastboot flash recovery twrp-2.8.6.0-m8.img
(You can copy and paste that command line. Command window, alt+space for menu, E for edit, paste.)
After some bytes transfer and it says OKAY, go to phone.
Choose to go to HBOOT and then RECOVERY.
Make a nandroid backup before attempting root - an absolutely essential step - stop and do so now. The defaults under Backup in TWRP are just fine for this. Optionally, check the box to turn on compression.
When done, Install - navigate to the SuperSU zip you placed on your storage earlier and follow the on screen prompts.
Reboot, profit, you're backed up, rooted and you now have the right tools.
Optionally - go back into TWRP again, make a nandroid backup of your rooted version. (I always do.)
Let me know if you have any questions.