V + 다가 connects two related actions that occur in sequence, with the second action typically interrupting or contrasting with the first. It is most often used with 갔다, 왔다 and 있다 -- the latter translates as 'and later on' (lit: and then after existing):
친구가 한국에 2년 동안 있다가 나갈 것이라고 했어요.
My friend said that in two years he will leave Korea.
친구의 생일 파티에 갔다가 저는 취하도록 술을 마셨어요.
I went to my friend's birthday party and drank to the point that I was drunk.
학생들은 교실에 늦게 왔다가 일찍 갔어요.
The students came to the classroom late and left early.
저는 초등학교 선생님 이었다가 진로를 바꿨어요.
I was a primary school teacher and then I changed my career.
V + 고는 is used between two clauses to show that links one action to another subsequent one. The action in the first clause (in present tense) is completed and the second is the outcome or consequence (in past tense). In this structure the consequence is always emphasised and can sometimes be surprising:
이 신발을 사고는 지금까지 안 신었어요.
I bought these shoes and then I didn't wear them.
아내가 저를 매섭게 노려보고는 방에 나갔어요.
My wife scowled at me and then left the room.
그가 저를 보고는 놀라지 않았어요.
He wasn't surprised to see me.
(He saw me and then he wasn't surprised).
재킷을 벗기고는 가장 좋아하는 자리에 앉았어요.
He took off his jacket and sat in his favourite chair.
그가 창문 밖을 바라보고는 울기 시작했어요.
He stared out of the window and started crying.