Pop songs rarely modulate, and if they do, usually modulate by step, so just find the root note and you have the key. Gangnam Style doesn't have any modulations

Pop songs rarely modulate, and if they do, usually modulate by step, so just find the root note and you have the key. Gangnam Style doesn't have any modulations unless you count the major I as a modulation. It definitely jumps out to the ear as something unusual. For classical music the working key is constantly changing and often two theorists would disagree on the "harmonic meaning" of a passage. One telltale sign of a key change is an x-V-I progression (in the new key) where x is any secondary chord that leads naturally into the V. Bonus points if the x or the V don't work in the old key; if you're in C major and you hear a D7, you know something's up.