Depending on which country you're watching from, the YouTube app may or may not be available for your Fire TV device. If you can access the YouTube app, this is the simplest way of watching YouTube videos on your device. If not, there are ways around this problem. You can use a browser app on your Fire TV device to navigate to YouTube and watch videos that way. Plus, some Amazon Fire devices allow you to cast media to your TV, so you can open a YouTube video on your phone or tablet and cast it to the big screen.