The most convenient route, if traveling by public transport, is to travel by train from Dublin’s Heuston station. This is accessible by tram (the Red Line Luas) or by local city bus. You can pre-book your train tickets from Irish Rail.
There are very few direct trains from Dublin to Millstreet, most will be the Dublin – Cork train service with a change in Mallow where you will catch the train towards Tralee (this also serves Killarney). We strongly advise that you book your train trip before arrival in Ireland to ensure that you have a seat!
To get a public bus from Dublin to Millstreet is almost the same price as train if booking in advance, taking much longer, and requiring more changes. You cannot buy bus tickets all the way to Millstreet online. However, if you are arriving early into Ireland (or leaving late) there are buses that connect Dublin Airport with Cork city that you may wish to consider, including the Aircoach - this is cheaper than the Dublin - Cork train, but you will still need to make your way from Cork City to the site.