This is surprisingly one of the most frequently asked questions we get. Please take a look at this picture and look out for the blue New Thread button on the mid-left side of the screen:
You *MUST* be logged in to start a thread - this obviously enough means that you must have a Boards.ie account to start a thread. You'll know you're logged in in the second area on the upper right that I've highlighted with "your name here" in it.
You can only start a new thread when viewing a forum, not when you're reading a thread.
Finally, there is no "New Thread" button on our front page which seems to confuse a lot of people, but having one there makes no sense as the front page is not a forum, merely a listing of the most recent threads on the site across all forums.