The basic construction for saying “to do something” is [object] + -을/를 (= object marker) +
하다 (= to do), and to this, you add 잘 [jal] or 못 [mot].
~을/를 잘 하다 = to be good at ~ (lit. to do ~ well)
~을/를 못 하다 = to be poor at ~ (lit. to do ~ poorly)
Example
노래 [no-rae] = singing, song
노래를 잘 하다 [no-rae-reul jal ha-da] = to be good at singing, to sing well
But since 못 하다 can also mean “to be unable to do” something or “can not do” something, 잘 [jal] is often added in front of this and makes it 잘 못 하다, to make the meaning clear. By saying 잘 못 하다, you literally say that you “can not do something well” or “are unable to do something well”, which is similar to being poor at it.
Are 잘 and 못 (or 잘 못) only used with -하다 verbs?
No.
TravellingWithWords 