Intro:

At first when lollipop came out for the LG G3 there wasnt a root method and people had to use LG G3 flash recovery to go back to 4.x to root and then with their root install a 5.x rom – that was a pain (never had to deal with that pain). And then this root method came out:

All of these links explain how to root it using manual method (its all the same method as I understand):
*https://www.reddit.com/r/LGG3/comments/2ydptk/workinghow_to_lollipop_root/
*http://www.droidviews.com/easily-root-lg-g-flex-2-and-lg-g2-g3-g-pro-2-on-lollipop/
*http://forum.xda-developers.com/android/development/guide-root-method-lg-devices-t3049772

A user on the threads made an installable program of this same method that can do all of this very nicely.

How to root:

Step 1. PREPARE PC
All you need to do before it is to install LG G3 USB Drivers from here http://androidxda.com/download-lg-usb-drivers (you will mmost likely need to install the LG G3 “(all variants)” )
Step 2. ROOT – go to this link:
http://www.droidviews.com/easily-root-lg-devices-using-the-one-click-root-script/
Step 3. VERIFY
Install “Root Checker” from the play store to verify you have been rooted. (run it and it will tell you)

The rooting app doesnt do this next part of installing TWRP for you. You have to get another program for that… read on…

How to install TWRP:

This is Optional – if you want to install roms, then you should install TWRP. If your fine running stock & rooted then your set and you can quit reading ahead.
How to install the Recovery (so that you can install roms):
http://www.droidviews.com/root-att-lg-g3-d850-and-install-twrp-recovery/
SUMMARY OF ARTICLE: All you need to do is find in the play store “D850 Auto Rec” and run it. On first launch it will make a backup. then press Flash TWRP and your good to go. Also install “Quick Boot” and from that app you can boot into recovery without having to boot into recovery using the manual method (note that the grey box is the selection box, not the white one)

If you also want to install a Rom (such as Cyanogen mod):

Check out this site: https://www.reddit.com/r/LGG3/comments/33r0xn/updated_method_to_root_install_twrp_and/ The first 2 steps are about setting up root and TWRP. Over here rooting with method2 is the same method that I mentioned. Both of his TWRP install methods work, however I just looked up “auto rec d850” in the play store and installed that. After he covers installing Cyanogenmod and other mods using an application. However you can also use the manual method via TWRP.

How to unroot it:

Havent tried it.
http://www.droidviews.com/how-to-unroot-android-devices-manually/

Whats the difference between PA-Gapps and regular Gapps:

PA-Gapps are no longer made as their developer retired (his final post). However they are available in that same final post link. Gapps on the cyanogenmod website are the newer ones. To see the difference read this.