~도 돼요? & ~면 안 돼요?

To ask permission, use this lovely little guy <동사> + 도 되다 If unsure when to use 되 or 돼 check what I wrote and it might help ^^

Examples:

창문을 열어도 돼요?
Can I open the window?

책 읽어도 돼?
Can I read a book now?

이 빵을 먹어도 되지?
I can eat this bread, right?

선생님, 집으로 가도 돼요?
Teacher, can I go home now?

A similar expression is ~면 안 되다 which is refusing permission. When used in a declarative sentence, it stands for refusal such as:

여기 담배를 피우면 안 돼요 (There's no smoking here)

However, it is also a way of expressing a desire to do something. This has kind of a linguistic baggage to it. You are wanting to do something but are checking to see if it's okay before you proceed. You are expecting the answer to be "sure! go ahead" but you're just checking. You also may just be asking out of politeness. It can go both ways so use your politeness in your tone.

Examples:

지금 자면 안 돼요?
(you mean to tell me that) I can't sleep now? [Can't I just go to sleep?]

먹으면 안 돼요?
I can't eat this? [what do you mean I can't eat this?]

여기 차를 세우면 안 돼요?
I can't park my car here? [so where else might I park it if not here?]

같이 가면 안 돼요?
We can't just go together?