Taking the bus strikes into account...
For those arriving by Ferry to Dun Laoghaire Port:There is a DART station (intercity train) right by Dun Laoghaire Port - ask anyone nearby or working and they will send you in the right direction. The stop you're looking for to get to the stadium is called Lansdowne Road and is 7 stops after you get on (should take no more than 20 minutes once you are on the DART and there is one every approx. 15 minutes).
Here is a map of the DART so you can familiarise yourself if you need to.
For those arriving by Ferry to Dublin Port:You could walk about 25 minutes to Tara Street DART station (use google maps for this but it's a very straight forward walk literally just stick to the quays and it's on your left eventually). If you do this it's only 3 stops until you're at Lansdowne Road DART station (see map above).
Otherwise, I would recommend getting a taxi. Would cost 15 and would have you there in 5 - 10 minutes.
For those arriving at Dublin Airport:Especially if the bus strikes are ongoing, the best way into the city and beyond is Aircoach (a privately operated bus service from the airport to various destinations). An adult return is between 10 - 14 depending on where you get off and the return journey has no expiry date (i.e doesn't need to be used the same day).
They normally operate a service directly to Ballsbridge, right next to the stadium, but this is suspended at the moment so... Either get it into the city centre and get a dart from Tara Street, or get the aircoach to
Morehampton Road in Donybrook and walk 10 mins max to the stadium (again go with google maps for this). Feel free to PM me if you have any questions on that.
By the way - DART costs between 2.50 and 4 for a single depending on what stop you are going from.