This guide is for never-rooted 2014 Fire HDs. Don't use it on any 2015 (5th gen) Fire. If your Fire has an sd card slot, go here.
Mar 3 Update: This guide is out of date. It could brick you! Don't use it!
Instead, follow one of these guides:
This explains how to use the Fire HD tools (for Windows) to root and install Gapps and a custom launcher on the Fire HD 6 or 7.
Note: If your tablet has an SD card slot, it's a 2015 Fire. Don't use this guide. Go to the 2015 Fire forums.
Download the latest tools from the AFH link near end of post. It includes the changes in the attached "jobs" zip. You only need "jobs" if you downloaded the tools before May 11
EDIT May 29: Playstore is currently unreliable. Until updated, use th...
I was able to follow those steps and TWRP appears to be working! I haven't attempted the update process yet since I want to be thorough so if you want to post some step by steps that are clear and precise I'd be in your debt yet again. :D
TWRP (Team Win Recovery Project) replaces a device's stock recovery and provides, among other options, the ability to install img (image) and zip files. TWRP for the Fire HDs was developed by JMZ and is described here.
How to install TWRP