There are lots of ferry services between Ireland and the UK.
From England: Ferries from Liverpool go to Dublin port.
From Wales: Ferries from Holyhead go to both Dublin port and to Dun Laoghaire while ferries from Fishguard and Pembroke go to Rosslare. The Cork to Swansea service has been sporadic over the last number of years and is currently not in operation.
From Scotland: we recommend that you take a ferry to Northern Ireland (to either Larne or Belfast) and then travel through Ireland. If doing this portion by public transport, connections in Larne are slightly easier as there is a train station beside Larne port, whereas you will need to make your own connections from Belfast port to the public transport network, then the bus/train to Dublin and follow the directions from the other articles here.
Dublin city centre - the Luas tram from Connolly train station, or, more frequently and about 30 metres of a walk from the Connolly stop, Busaras (Dublin central bus station) to Heuston station.
From France: There are ferries from Roscoff and Cherbourg to Rosslare Europort and from Roscoff to Cork.
If arriving into Rosslare Europort, and expecting to travel onwards by public transport, be warned about the trains! You will need to get a train up to Dublin then change from one station to another in Dublin to travel back to Millstreet. If you get the bus, you will need travel via Cork – this will take at least 6.5 hours, and may take over 9 hours. As such, we do not recommend arriving in Ireland via Rosslare if you are dependent on public transport.