I have not tested the hack myself but it seems relatively straightforward. As a first step you'll need to download and the install the Android SDK on your computer. Next you'll have to download the required files, unZIP them, and then use ADB to perform the hack. Your tablet is also going to have to be plugged into the USB port while you're attempting the hack.
Once you've hacked your KFHD you will have the option of installing apps which require root. This isn't something the average user will need, but it is the first step towards giving the KFHD all sorts of new features that aren't Amazon approved, including getting rid of the exiting home screen and the annoying ads on the lock screen. But there's also a better than even chance that in the next firmware update Amazon will fix the exploit that this hack needs, and I bet it will be gone before the larger 8.9" KFHD is shipped in November.
If you're wondering how this was possible with the locked bootloader, the answer is simple. They have little to do with each other. Rooting an Android tablet means that you have admin level access of the device. You can change setting and install apps not approved by the manufacturer.
The locked bootloader will only impact your shenanigans the next time you reboot the tablet. It
will reset some or all of the settings changed after you rooted the tablet, and it is also the first stumbling block on the road to installing another Android firmware on the tablet like Cyanogen Mod.