Follow the sign from the arrival terminal that reads, "Taxis and Car Parks and Exit." Exit the arrival terminal to the outside.
Cross the street and enter the building whose signs read, "Dublin bus, Car Hire, Coach Park and Hotel Shuttle Bus." Pass through this building to the airport's exit.
Cross the street and follow the signs to "New Coach Park," where the buses are parked.
Board the Flybus, which you will find in one of the bus stalls. You can purchase tickets onboard the bus for either one-way or round trips. The bus leaves from the airport every hour on the quarter hour (i.e. 10:15, 11:15 and so on).
Exit the bus at Tallaght Square. You will use this same terminal for the return trip, which also leaves every hour on the quarter hour.