Want, can, must

Want: -고 싶다

-고 싶어요 says what you want to do, and asks what the listener wants. For someone else, Korean says they "show they want": -고 싶어해요.

• 한국에 가고 싶어요.
  hanguge gago sipeoyo.
  I want to go to Korea.
• 뭐 먹고 싶어요?
  mwo meokgo sipeoyo?
  What do you want to eat?
• 동생이 강아지를 키우고 싶어해요.
  dongsaengi gangajireul kiugo sipeohaeyo.
  My little brother wants a puppy.

For a thing, name what you want to do with it (커피 마시고 싶어요 "I want some coffee"), or ask for it with 주세요.

Can: -(으)ㄹ 수 있다

수 means "a way", so -(으)ㄹ 수 있다 is "there's a way to": ability or possibility. Its negative is -(으)ㄹ 수 없다, or 못 (Saying no). For a learned skill, -(으)ㄹ 줄 알다 "to know how to" is common.

• 한국어를 조금 할 수 있어요.
  hangugeoreul jogeum hal su isseoyo.
  I can speak a little Korean.
• 내일은 갈 수 없어요.
  naeireun gal su eopseoyo.
  I can't go tomorrow.
• 김치를 만들 줄 알아요?
  gimchireul mandeul jul arayo?
  Do you know how to make kimchi?

Must: -아/어야 하다

The 아/어 form with -야 and 하다 means "must, have to". In speech 되다 often takes 하다's place: 가야 돼요.

• 내일 일찍 일어나야 해요.
  naeil iljjik ireonaya haeyo.
  I have to get up early tomorrow.
• 지금 가야 돼요.
  jigeum gaya dwaeyo.
  I have to go now.

May and must not

-아/어도 되다, "it's fine even if you do", asks or gives permission. -(으)면 안 되다, "it's not fine if you do", forbids:

• 창문을 열어도 돼요?
  changmuneul yeoreodo dwaeyo?
  May I open the window?
• 여기서 담배를 피우면 안 돼요.
  yeogiseo dambaereul piumyeon an dwaeyo.
  You can't smoke here.
• 내일은 안 와도 돼요.
  naeireun an wado dwaeyo.
  You don't have to come tomorrow.