When you are working with a discussion-type assignment, you will see a separate Group Discussion tab. Click this tab to access the group discussion thread.
You will see the list of discussion participants on the right, and the discussion thread on the left. In this thread, your instructor and peers will see your posts, and you will see theirs. You can add new posts from here (by typing in the Write Something… box), as well as reply to any existing post (by clicking the Reply link).