When the page loads, include a Javascript variable to indicate the "last item seen" or a time stamp (which I believe Twitter does as it orders the tweets in date order). You then have a Javascript function initiated by the setTimeout function which polls your server with this timestamp.
Your server then looks up to see if there has been any more posts since that point and if there has been, returns the number of results to the Javascript with an instruction to show a "See more" prompt - it also includes a new timestamp (if there are no new results, it just returns a timestamp).
Clicking on the "See more" prompt will then load in the new posts via Javascript, display them via the DOM and then reset the Javascript variable and repeat the process.
Of course, how you actually implement this will depend on how your data is structured, the server software you are actually using, what you actually want to do on the client side if there are new posts and then have often you want to "poll" the server for new responses (baring in mind more frequent polls will increase your server load).