Determine which point is nearest to your present location in Ireland where you can cross the Irish Sea via ferry to reach Wales--Rosslare, Dublin City, Dun Laoghaire or Cork.
Book train travel reservations with the Irish Rail to get to the ferry launch destination determined in Step 1 (see Resources).
Book your ferry reservation with the Stena Line if boarding the ferry from Dun Laoghaire, Dublin Port or the Rosslare route to Fishguard, by visiting the link for "Ferries to Wales" given under Resources.
Reserve ferry passage with Irish Ferries if leaving Ireland from Dublin City or the Rosslare route to Pembroke.
Make reservations with Swansea Cork Ferries if leaving from Cork to Swansea.
Be sure to keep all confirmation/reference numbers given to you when you book both your train and ferry accommodations. This information will be required in the event you need to reschedule or cancel your reservations. Note that a small charge may apply in either case.
Savor local flavor during your train ride. Wales is known for several gastronomical specialties, a few of which you may be able to enjoy in your train's dining car.
Listen with both ears during your ride. Welsh is spoken by at least 20% of the population. Fortunately, the wide majority speak primarily English, making you feel right at home.