Hi, I am from Dublin and have the following recommendations for travelling around Dublin and the rest of Ireland.
From Dublin Airport to Dublin City:
* Taxi - Depending on the number of persons, a taxi journey to the city centre will cost approximately EUR25. The journey should take 20minutes off peak.
* Aircoach - Luxury coach to city centre. EUR7 single and EUR12 return.
http://www.aircoach.ie
* Dublin Bus - EUR6 single and EUR10 return.
http://www.dublinbus.ie
Getting Around Dublin:
* DART - Dublin Area Rapid Transport. Rail network that services nothern and southern suburbs and city centre. Connolly Sstation if the main city centre station.
http://www.irishrail.ie
* Dublin Bus - Many routes that service suburbs and city centre.
* Luas - Two tram networks linking suburbs to city centre.
http://www.luas.ie
Travelling outside of Dublin:
* Irish Rail - Rail network that connects Dublin city with main Irish towns and cities.
http://www.irishrail.ie
* Bus Eireann - Bus srvices that connects all major Irish towns, villages and cities.
http://www.buseireann.ie
Car Rental - My favourite choice. In order to see the best of Ireland (small villages, scenic areas) car rental is a must. Very cheap so why not!
http://www.carrentaldublin.ie
Anyway, let me know what you think of my recommendations.
Best of luck!