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Like Peter mentioned, Korean 조사 is really tricky and it's safer to stick with the polite form.
Here are some rules of thumb, but I'm hesitant to call them "rules" because there are quite a lot of exceptions:
1) In writing, 조사 is almost never omitted.
2) Conversely, in speech, 조사 is almost always omitted, unless you're being formal (job interviews, presentations, business meetings... you see the point).
3) But, even in casual speech, 조사 is used when you want to EMPHASIZE.
A. Topic particles = Using it emphasizes "unlike other things," "as for ~"
B. Subject particles = Using it emphasizes you're talking about "none other than the subject itself."
C. Object particles = You use it when your object is far, far away from the verb, and you want to make sure to mark an object to avoid confusion.
Examples:
A.
내일 나 일해. Tomorrow I work.
내일*은* 나 일해. As for tomorrow, I work. (But probably not today, or the day after tomorrow..)
B.
나 이거 만들었어. I made this.
내*가* 이거 만들었어. I made this (,not somebody else).
C.
쿠키 먹었어. I ate cookies.
쿠키(를) 어제부터 오늘까지 계속 먹었어. (Here, the object "쿠키" is so far way from the verb "먹었어" so you can use the object particle to make sure to mark the object. But then again, you don't have to.)
Bottom line:
1) In writing or formal speech: Use all the particles.
2) In casual speech: Drop the particles, unless you want to emphasize.
