you can take a very cheap ferry (by foot or car) from or to Holyhead in Wales - Dun Laoghaire. it takes 90min and costs return only 21 Pounds (circa 33 Euro)
the ferry is very compfi and a quick trip between both countries.
Dun Laoghaire can be reached easily from Dublin in about 20 minutes by DART train. The station leaves you in the centre of town beside the ferry terminal (for those wanting to go to Holyhead in Wales). You can also stay on and get off at Glasthule/Sandycove if you want to visit the Joyce tower and don't want to walk from Dun Laoghaire.
Plenty of buses come from town to Dun Laoghaire, with the 46A and 7 being the most frequent. They can usually be caught from around Trinity College in the city centre and will take anywhere from 30-45 minutes depending on traffic. Personally I'd take the train if I were you :-)
The Dart is the quick, regular train service that runs from Howth island all the way down to Greystones, south of Dublin.
If you come in by train, bus or ferry, this is the travel hub of Dun Laoghaire. You’re right in the middle of things here and all shops and amenities are within comfortable walking distance.