I have no idea it must be their profession

By singing

Oh, I don't know... Maybe with their vocal cords like most people do? Just a thought. :)

Can this also mean something like, "How well does that singer sing?"

They sing by screaming at the top of their lungs!!

Is it possible to put 어떻게 in front or would that interrupt the sentence structure?

Vocal cords

I have no idea it must be their profession

Why can't it be "how does that singer over there sing?"

Trolololololololol hahahahaaaaaaaaaaa. That's how.

With his/her voice lmfao

from his heart?

Shouldn't "How does the singer sing" also work?

Is this question asking more like how physically the singer sings, like how they are able to ("how can they do that?"), or asking in what way it is they sing like; "are they good or bad," "do they have a high voice," etc?