"How do you keep busy?" -- 한국말로 뭐예요?
In English, it's common to ask "How do you keep busy?" if you don't know whether a person is a student or has a job.
I know the phrases 직업이 뭐예요? and 무슨 일 하세요? -- are these the only common expressions?

Question

"How do you keep busy?" -- 한국말로 뭐예요?
In English, it's common to ask "How do you keep busy?" if you don't know whether a person is a student or has a job. 
I know the phrases 직업이 뭐예요? and 무슨 일 하세요? -- are these the only common expressions?

Answer

I'm happy to help! ^^

Answer

It's really nice for you to explain the meaning of your question.

I can learn English while I am on your question.

Answer

"어떤(무슨) 일 하고 있어요?"  도 좋아요.

Answer

Hi~

Yes, 직업이 뭐예요 and 무슨일 하세요 both are used frequently. 
I think  보통 뭐 하세요? would be a good substitute for "how do you keep busy".

Hope this helps :)