Hi Emily,
There are a couple of bus/coach providers that operate direct from
Dublin Airport to Limerick that would be the best option, as there is no train service from the airport.
City Link service 712 and
Flight Link 723 service, both operate from the airport, and tickets can be booked online through their websites. 🚌
If you wish to take the train, you would need to go into the
city by bus and then use the Irish Rail service from
Dublin Heuston Station. 🚆
Transport for Ireland has a handy journey planner for looking up providers and services for this and any other public transport journey you may have.
Hopefully, this will help with your transport plans, and you have a great time in Limerick! ☘️