This is a quick guide how to root your P8. Please note that this is for the standard P8 only, it will NOT work on the P8 Lite or P8 Max.
WHILE THIS SHOULD WORK, THERE IS NO GUARANTEE THAT IT WILL AND THERE IS ABSOLUTELY NO WARRANTY IF SOMETHING GOES WRONG! YOU DO THIS ON YOUR OWN RISK, AND IF UNSURE, BETTER NOT DO IT!
Prerequisites:You need an unlocked Bootloader (see here) and a working adb+fastboot environment.
Chainfire's SuperSu zip
1. Put all the Downloads into a folder and open a terminal in that folder.
2. Reboot into the bootloader via 'adb reboot-bootloader' (all commands without the quotes).
3. Flash the TWRP custom recovery via 'fastboot flash recovery openrecovery-twrp-22.214.171.124-p8-x.x-xx.img' (replace this with the correct name).
4. Boot into recovery by pressing the Power button and both Vol+ and Vol- during powerup (don't use 'adb reboot recovery'!).
5. Copy the SuperSu ZIP to your internal storage or MicroSD card (If you have trouble connecting to the recovery on Windows, try Koush's Universal ADB Driver)
6. Select 'Install' in TWRP and pick the SuperSu ZIP in the file picker and then swipe to confirm flash. Reboot and you have root!