은/는 커녕 is used to say “There wasn’t X, let alone Y” or “Never mind Y, I didn’t even do X!” The noun or verb before the structure is attached to let alone or never mind, while 도 is used for emphasis in the second part.
Note that if X is a verb, you have to nounify with the 기 construct added to the verb stem.
For the example sentences, you have many in above links, but I’ll add a few from endic.naver.com as I’ve found myself to use this dictionary more and more to find out how words are used in context based on realistic native sentences.
그 녀석 불어는커녕 영어도 못한다: He knows no English, to say nothing of French.
그는 죽기는 커녕 다치지도 않았다: He didn‘t die, he wasn‘t even wounded.
손님커녕 우리 쓸 공간도 충분치가 않다: There isn’t enough room for us, let alone any guests.