How much notice do you have to give to leave a goshiwon?

One month is the standard, and since there is no contract you should confirm it in writing now rather than when you want to leave.

The normal arrangement: you tell the operator at least one month before you intend to go. So to leave at the end of next month, you tell them before the end of this month. Some buildings ask for two weeks, a few ask for a full month from the date you give notice rather than from month end.

What to do today: send a KakaoTalk message asking "퇴실할 때 얼마 전에 말해야 해요?" — how far in advance do I need to give notice. Their reply is your record, and it costs you nothing to have it before you need it.

When you do want to leave:

1. Give notice in writing, not verbally. KakaoTalk is fine and is what everyone uses. State the exact date you will move out.
2. Ask them to confirm the date and whether anything is owed or refundable.
3. Photograph the room when you leave, empty and clean. This is your protection against a cleaning or damage charge, the same as any rental.
4. Return the key or key card and get confirmation. If there was a key deposit, this is when you get it back.

What happens if you give short notice: with no deposit there is nothing for them to withhold, so in practice the consequence is losing the remainder of a month you already paid for. It is not a legal problem, it is a money one.

And the reason this matters more than it sounds: leaving properly with notice means you can use that operator as a reference or come back later, and in a student district where buildings talk to each other that is worth something. It costs one message a month ahead.