A lot of people here are not understanding the difference between rooting their Kindle and sideloading apps to it, so I'd like to make things a little clearer.
First, you need to know how the device is setup. Like computers, the Android OS is divided into folders that are hidden. Only leaving you with access to your external and internal SD cards. Comparing it to Windows, this would be the same as hiding your C:\ drive and only giving you access to your documents, music, videos, desktop, CD/DVD, and external drives.
However, like in Windows, Android apps still have access to that "drive" but only part of it. Windows applications are pushed to the Program Files
folder and Android apps are pushed to the Data
folder. The only part that can be written to by apps when you're not rooted OR have administration rights.
Being rooted means you have administration rights.
It means that you can go into any folder, add things, move things, and delete things. In the Kindle's case, this would allow you to remove any bloatware like comiXology, IMDB, Facebook, and Quickoffice that are in the /system/app/ folders. And because Google Apps require framework to work, you have to install it as a system app.
You can sideload most apps by just sticking it in your SD card and using something like ES Explorer to install it. However, this is limited by the Google framework some apps require for billing processing upgrades and currency. Hence sometimes they don't work. Like every other app, they all go to the Data
Do NOT root your device unless you find a specific app that tells you you NEED to be rooted. For the most part, those will be apps like keyboards, system tweaks, and things most of us don't need on stock anyway. There's always alternatives to everything, so just look around.
Here is a list of app markets that work with the Kindle Fire. You do not need anything special to use them, and you can even just use the Silk Browser for those that don't have their own APK storefront.