You will need to first install the Amazon app store on your Android device. To do that visit https://www.amazon.co.uk/androidapp in the browser on your device and download the app.
The app store does require you to enable "unknown sources" or it won't install. This Amazon page says how to do that in older devices https://www.amazon.co.uk/gp/feature.html?docId=1000851343
On newer devices just download the app, then you will get a message you need to enable unknown sources. Follow the link on your device (takes you to settings), enable it and then it'll install.