Here're some simple sentences with markers:
A : (glancing at people who came to the party) 다 왔어? Did everybody come?
B : 철수는 안 왔어. Chol-su didn't come.
You can take B's statement as "(As opposed to others), 철수 didn't come.", everybody but 철수 came.
A : Who spilt coffee on my laptop!!!
B₁: 내가 안 그랬어. I didn't do it. (Literally, "It's I who didn't do it")
B₂: 난 안 그랬어. (As opposed to others,) I didn't do it.
B₃: 나 안 그랬어. I didn't do it.
B₃'s statement is most neutral, it's not implying that somebody else did it. That's why it's safer to just omit the marker if you're not sure.
When you introduce something or someone, you'll always use the topic marker.
전 소민이에요. I'm So-min.
이 분은 제 할머니세요. This person is my grandmother.
이건 제 그림이에요. This is my painting.
When you say something opposed to someone's statement, you'll use the topic marker.
A : I think they're stupid.
B : 난 그렇게 생각 안 해. I don't think so. (As opposed to you,) I don't think so.
When you repeat what someone has just said because you're amazed or surprised, you'll use the identifier, 이/가.
A : 이거 내가 그렸어. This thing I painted. ("I painted this thing(picture)")
B : 너가 그렸다고? Are you saying you painted it?
A : 쟤 내 남자친구야. He's my boyfriend.
B : 쟤가 남자친구라고? Are you saying he's your boyfriend?