How to download incompatible or restricted Android apps from Google Play

Sometimes you find that Android app you've been longing for, but Google Play won't let you download it for whatever reason. Maybe it thinks your device is outdated, or you happen to be in the wrong country. Anyway, this isn't something you'd expect from Android, the land of the free, right? Nuh-uh! Of course there's a way to work around that if you happen to want a particular app so badly! At least three ways, in fact!