Amazon doesn't offer everything you want in its Kindle marketplace. Fortunately, some of the apps it doesn't can be downloaded from the company that makes them, or from a third-party app store.
Before we tell you how, here is one warning. Don't go dashing around downloading just anything from anywhere, because there is malware in the wild for Android (and Kindle Fire) devices, and it sometimes gets distributed by being hidden in an app.
If you get an app from a third-party source, make sure it's an app that you want, and that you're getting it from a reputable app store or manufacturer. One way to check is to read the reviews, and make sure that you're only getting things that are well tested and respected.
To install from another source than Amazon's App Store:
1. Go to your Settings for your Kindle Fire. That's the Gear icon (older devices) or the slider that you pull down from the top.
Tap More for the Settings page.
2. Set Your Kindle to Allow non-Amazon apps to be Installed.
Tap Device. Toggle the setting labeled Allow Installation of Applications to On. This enables your device to install apps not in Amazon's Appstore. If you have a different version of the Kindle Fire than I have, you may find this setting under Applications.
3. Now, using the web browser, go to the third-party app store or manufacturer's site to get your app.
Unfortunately, this won't work on Google Play with a Kindle Fire. If you select an app there, you may be told "it will be installed soon," but in fact, it never will be on a Kindle Fire. Google Play Services also are not supported on the Kindle Fire, so you won't be able to use Google's YouTube app or other Google apps that require these services.
However, you can use Google Play to check the description and cost of the "real" app, and also all the details, before you download it from another place. Not all app stores are curated (and reviewed for malware) as well as Google Play and Amazon, and Google Play is the other "official" app store.
Some third-party app stores include:
We'll end with a video showing you how to install the 1Mobile Store as an alternate store on your Kindle Fire. If you choose to do this, you won't have to use the web browser to go to the site -- you can just open the 1Mobile store.
Re-Lock your Kindle Fire
For safety's sake, you may want to keep the Allow Installation of Applications set to Off when you're not planning to download. It prevents the possibily of your accidentally downloading something you didn't want.