Hi Rawin,
This is a very tricky area in Korean. As far as I have been told, 은/는 has 3 main roles, and 2 of them are connected. That is, 은/는 for emphasis, and 은/는 acting like 'the' in English to refer to something we have already mentioned. For example, 어제 이곳에서 립아이를 먹었는데 고기는 부드럽고 맛있었다. Here we are emphasising "meat" by mentioning it again (I ate ribeye here yesterday, and the meat was soft and delicious).
The 3rd usage I believe is with complementation - so in a sentence like "I know that John likes her" - the "I" subject is in the 은/는 form, and the complement 'John likes her' uses the 이/가 form - honestly, I am not 100% with this form, because what is complementation in English may not be complementation in Korean so I just go with what feels right, and hope to get corrected when I am wrong (which is a lot haha)
A lot of reading helps - newspapers, books etc - to get a feel for it.
Good luck with your exam