I need to understand some moderation rules applicable to me. Currently, when for other peoples post, i don't see any close button. All i can do is either downvote or flag the post. If i feel that question doesn't belong to this site, Should i flag it or downvote to recommend closing the question ?
From the FAQ
250 Vote to close, reopen, or migrate your questions
300 Create new tags
500 Retag questions
1000 Show total up and down vote counts
2000 Edit other people’s posts, vote to approve or reject suggested edits
3000 Vote to close, reopen, or migrate any questions
I hate to say it, but seriously - read the whole FAQ. :) Clicking on each header expands it so you see the whole section (and doing all of them, gets you a badge).
And yes, if you think a Question should be closed - flag it.