Does anyone know where these tickets are sold? I cannot find any information. On the website it's written that you can buy them online but it's a lie.
As far as I know, DART tickets cannot be bought online, and it makes no sense to do so as those are commuter trains (this includes one to Howth). There are no reserved seats, and lots of standing space there. Buy them on station from the machine. Their price is fixed.
However, you can indeed buy long distance IrishRail tickets online (such as Dublin-Cork or Dublin-Limerick). Note that you still won't get the actual tickets - instead you'll get a number which you need to type into the ticket machine on a train station, and the machine will give you the actual ticket. Thus you're not going to save time. However you might save money - as for those (and only those) tickets you can get much better price if you book sufficiently in advance.