Here's a brief introduction of 이/가 vs 은/는.
이/가 marks the subject ("subject marker") of a sentence like in other languages.
- 차가 온다: A car is coming. (no special connotation but a simple factual statement)
은/는 is "topic marker", but it often doubles up as the subject of a sentence as well. When the subject is marked with 은/는, it has the connotation of expounding it, drawing the listener's attention in order to say more about it.
* 나는 학생이다. I am a student. (It has the nuance of starting a discourse on 나)
It can also start a compound sentence which employs a full [subject+predicate] clause.
* 나는 키가 크다. As for me, my stature is high (describes 나 using a full clause 키가 크다)
(나: topic as well as subject of main clause, 키: subject of subordinate clause)
To say the same thing in English, one would use "As for me, ..." which starts to talk about "me". So we can say 이/가 brings a focus to the noun before the particle, while 은/는 directs attention to the information coming after it.
은/는 is often used to make a statement of contrast.
* 그는 학교로 가고 나는 집에 왔다. He went to school and I came home.
The topic and subject marker can also work together to form a typical compound statement.
* 그가 왔을 때 나는 자고 있었다. When he came, I was sleeping.
(typical subordinate and main clause arrangement: 이/가 in sub-clause, 은/는 in main)
In a discourse, 이/가 tends to introduce a new subject, which corresponds to the use of indefinite article "a" in English. 은/는 statement(s) then says more about the new subject, as one would do using the definite article "the" in English.
1. 어제밤에 큰 불이 났다. A large fire broke out last night. ("이" corresponds to "A")
2. 그 불은 큰 피해를 가져왔다. The fire caused a substantial damage. ("은" to "The")
(#1 introduces a brand new subject, a fire, and #2 gives more detail on it)