Distance-wise, Dublin Airport to the city centre is about 12km (7.5 miles) and the trip will take anywhere from 30 minutes up to an hour, depending on the time of day and traffic. You'll note the word 'traffic', as bus, car and taxi are currently the only modes of transport to and from the airport into the city.
The easiest option would be to take a taxi, which can cost approximately €25-30, depending on time of day and traffic, and other various factors. You can check these out at Taxifarefinder
Another option would be to take the Airlink Express
, which services directly to Dublin's most popular locations. You can either catch the Airlink 747 or the Airlink 757 to the city centre, depending on the location of your accommodation. Ticket prices one-way are €7, or €6 if you buy them ahead of time here
A final option is the Aircoach
(or as locals call it, The Blue Bus), which services the city centre, as well as other areas around Dublin; useful, if you're staying somewhere outside of Dublin's central area. This service also costs €6
and there's no hassle with having to manage public transportation with your luggage. It runs every 15-30 minutes
with three main stops in the city centre: Drumcondra, O'Connell Street and Trinity College.
Hope this helps, and enjoy your break in Dublin!(Prices quoted are correct at time of publishing)