"Where do you put up?" is used to mean where are you staying temporarily, but it is more often used with an object: A: Where do you put up visiting relatives?

Where do you stay or where are you staying?

To “stay” in a place is to live in it temporarily. To ask someone where his permanent home is, you say: “Where do you live?” But if you meet someone who is on holiday, or is here temporarily, you ask: “Where are you staying?”.

How do you ask where do you live?

Usually, someone will ask you where you live as a polite question after they've asked you your name, where you're from, and what you do for a living. They'll say: “So where do you live?”