The "Reply" button at the bottom-right corner of each post will add a reply at the end of the thread while including that post's content as a quote. At the bottom-left corner at the end of a thread, however, the "Add Reply" button will add a post to the thread without quoting anything. So, there are the two ways to add more to a thread as you go along.

Starting a new thread such as "The story of my..." or whatever would be something you could decide to do, if you wish, and I believe you can change a thread title by changing the "Title:" line at the top of any post.