[Nexus 6 Q&A, Help & Troubleshooting] :
Sorry for my late reply. Was working till late yesterday and been preparing for a family event for later this evening. I'll try to explain more thoroughly:

c) Boot into Android normally. This means simply letting your phone start up and signing in if you haven't done it earlier. Then go to the system settings and scroll all the way down to "About Phone". Click that and in the following screen you will see several parts - one of which will be titled "Build number". Tap that 7 times. You will get a toast message on each tap eventually saying that "you are now a developer". This means that a new setting is activated. Go back to the settings front page and scroll down. Now a few steps above the "About Phone" section you will find a "Developer Options" section. Open that and scroll down to where it says OEM unlocking. Toggle it on. If you have a secure lock activated (PIN, pattern, password etc.) the phone will ask for your security code/pattern. Enter it and make sure the toggle is left ON before proceeding to do anything else.

Through the last steps from d to g I'm going to advice you to read these 3 threads. They have everything covered and you will learn a bit about what things like "fastboot" or others are all about.

1. http://xdaforums.com/nexus-6/general/guide-flash-factory-images-nexus-6shamu-t2954008

2. http://xdaforums.com/nexus-6/general/noob-read-adb-fastboot-how-help-t3006500

3. http://xdaforums.com/nexus-6/general/how-to-nexus-6-one-beginners-guide-t2948481

Once you have read these you should have a general image in your head about what I was talking about. You'll understand that fastboot is a tool to flash firmware partitions on the phone (it's also used to unlock the bootloader) and you'll figure that it works in a command shell and the commands almost always start with "fastboot flash XXX". You'll also understand how to use a fastboot command to make sure your drivers are working and that your computer recognizes your phone in bootloader mode. You'll figure that TWRP is a custom recovery and it's also installed via fastboot. And within the recovery, you can make backups, restore backups, wipe partitions and install custom roms/kernels/whatnot else.

Once you get the hang of it it really is quite simple. You simply use fastboot to flash a recovery and within the recovery is where you will perform most of the other stuff such as rooting and backing up the device. The various toolkits around here do exactly this but they have a premade UI that guides you step by step and do the commands for you. Unfortunately if you don't already know what you are doing, then in case of an error you won't know what to do to fix the problem. That is why I advice on reading the previous threads and if you want to be more sure of yourself go find a few youtube videos.

And if/when you hit problems come over here to those threads to see if anyone else has hit problems and how to fix them. I can assure you that pretty much every possible error and success has been covered somewhere here so there will also be a way to fix problems. The most important things as you read already are

1. TOGGLE THAT OEM UNLOCKING in settings -> developer options before doing anything

2. Once your bootloader is opened, DO NOT RELOCK IT unless absolutely necessary

With an unlocked bootloader you can fix pretty much every possible thing. Even faulty factory image installs or OTA updates gone wrong.