Too, also

저는 학생이에요 = I’m a student. 
저도 학생이에요 = I’m a student too. 

오늘 일해요? = Are you working today? 
오늘도 일해요? = Are you working today as well?  

내일 갈 거에요 = I will go tomorrow. 
내일도 갈 거에요 = I will go (again) tomorrow. 

도 with verbs. Add -기 to the verb stem to change verb into noun. noun form of verb + -도 하다 by adding 하다 you literally saying “to do + verb in noun form + also”. (to act in action, to sing into song.) 

가르치다 = to teach 
가르치기 도하다 = to also teach 
저는 영어를 가르쳐요. = I teach English. 
저는 영이도 가르쳐요 = (I am a science teacher) I teach ENGLISH as well.  
저는 학생이에요. 저는 영이를 가르치기도 해요.  = I am a student. I also TEACH English (work as an english teacher.)  

not only…but also

앤디는 한국어도 영어도 알아요 – Andy not only knows Korean, but also English.
그는 공부도 운동도 다 잘한다 – He is not only good at studying but also good at playing sports

Even 

그건 어린애도 알아요! – Even a child knows that!
아직 점심도 못먹었어? – You didn’t have even lunch yet?
우리집 강아지도 널 싫어해! – Even our puppy hates you!

Indeed

그 여자는 복도 많아요 – That woman has a lot of luck indeed
넌 소원도 참 많다 – You have many wishes indeed.

neither – nor

저는 동원 씨도 상우 씨도 좋아하지 않아요 – I like neither Dong Won nor Sang Woo.
나는 키가 크지도 않고 잘 생기지도 않았다 – I am neither tall nor handsome