To and From Dublin Airport, Dublin

Aircoach bus stops are right outside the arrival exit. They have several destinations, i.e., Cork, Belfast and Portaoise, so ask the ticketing staff where the Dublin City Centre bus stop is. The bus leaves every 10-20 min.
The ticket is 7euro one way, and 12 euro return. You can buy a ticket at the stops or online.

The bus to Dublin City Centre makes several stops including O'Connell St., near the Trinity College, and near the St. Stephen Green. Check online for route information to see which stop is close to your destination/hotel.

You can get on the bus to the airport in front of the Dublin Tourism Office on Suffolk St.

To get to and from Dublin Airport into the city I always take the bus. From outside the 'Arrivals' terminal you can take bus 747 or 748 into the city. It takes about half an hour to get to O'Connell Street from the airport and then another 5 minutes to get to the Central Bus Station.

Make sure you have correct fare on you (or have already bought your ticket from a machine near the exit of the Arrivals hall) to make boarding the bus easier, as there will usually be a crowd of people all trying to get on the bus.

Tickets:
Adult: EUR 5
Child: EUR 2

The website below has the timetable for route 747.

To and from the airport it is very convenient to use AirLink buses. When you go out of the arrival hall take the left exit and you will see the green double decker just outside. It takes about 30 - 35 minutes to the central bus station of Dublin, Busaras, which is the end stop. From the same spot you can take the bus back to the airport. The ticket is 6 Euro (February/March 2007).
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Update March 2013: Today I took the airport bus from O'Connell Street. To the airport it took 40 minutes and the price was still 6 Euro.

We decided to use the Airlink bus back to the aiport on our trip because it was economical and quite easy to use. The stop was conveniently located on O'Connell Street in front and it also stops in Busaras (main bus terminal).

The Airlink (Bus 747 and 748) runs service from the airport to the city center (and vice-versa) with serive every 10 minutes or so. The bus is a double decker bus and the trip takes about 20-30 minutes depending on what time of day you are using the bus.

When you arrive into Dublin Airport the Airlink is conveniently located outside the arrivals hall, you can't miss it, there are plenty of people probably waiting for it as well. Depending on which bus you take you will make either 2 or 3 stops.

The price for a one way ticket is 6 Euro (there is a discount if you buy a return). You can either purchase a ticket at the tourist information booth, at the kiosks located outside near the Airlink service or you can use coins of bills to pay once on board.

An underground railway line called 'Metro North' which will connect the airport to Swords and Dublin city centre has been approved and is in development. In the meantime, though, it is necessary to use other transportation options when traveling from the airport to the city centre.

After my arrival, I used the Air Coach service which charged a flat fee of 8 Euros. The Aircoach airport stop is located just outside the arrivals hall door. There was a representative present selling tickets and answering questions.

To get to my hotel near St. Stephens Green, I took the Leopardstown/Sandyford line. The hotel's web site said to get off at Kildare Street; however, the bus driver told me it would be easier to walk from the next stop at Lower Leeson Street. The driver even got out and pointed me in the right direction -- which was very helpful since it was my first time in Dublin.

When I get off the plane after a long flight I rarely feel like trying to figure out a new city's public transit and taxis are usually too expensive so when I landed in Dublin, I went looking for an airport shuttle. Aircoach provides regular service between the Dublin airport and most hotels downtown. All you need to do is buy a ticket from the counter that is located on the left as you exit the baggage claim area, tell them which hotel you're going to, and they'll let you know which bus you need to get on and where to stop. They run on fixed routes so you might have to walk a bit between the aircoach stop and your hotel, but in our case it was only a 5 min walk along St. Stephen's Green.

The price for a roundtrip ticket was 14 Euros. Aircoach stops are well identified so you don't have to worry about not knowing where to go to catch a shuttle back to the airport. The shuttles run every 10 min.

Getting to and from Dublin Airport must be unique in Europe.
There's an "Aircoach" that is excellent. It serves South Dublin much better than North Dublin.
Timetable and drop off / pick points can be see at
http://www.aircoach.ie/
There's an "Airlink", run by Dublin Bus that's very limited. Hardly surprising! Serves the Bus Station ( for buses throughout Ireland) and some of the rail stations ( for trains throughout Ireland). Not much use if your plans were to visit Dublin. The Bus Station is not in the most pleasant part of the City and the Rail Stations were built in the 19th Century, more with military / strategic objectives than convenience for a travelling populace and are for from central Dublin
Now here's a paradox.
You can also get a taxi. There always seems to be plenty of taxis at Dublin Airport and its reasonably quick however it is quite expensive. Allow 25 to 30 Euro for you journey to the north City or City centre and possibly 30 to 40 Euro to the south City.
Getting back to Dublin Airport is very difficult.
If you are convenient to a pick up point for the Aircoach, you can hardly do better.
Otherwise a taxi is probably the best, however if you try to book a taxi, early in the morning or during rush hour you might find a very negative attitude. Just keep phoning different "taxi companies" in the hope you will get a booking. You probably will, eventually.
If you're staying in a good hotel, they will probably have a taxi company they can call on with reliability, so ask the hotel to book one.

Airlink is the bus service offered by DublinBus to and from the Airport. It cost €6 one way or €10 round trip and is also included in the Rambler tickets.
There are other Dublin Buses that provide service to and from the Airport (such as the 16) but Airlink 747 is non-stop between the Airport and O'Connell St. and then to Connelly Station. Going to the Airport it also stops at Parnell Sq. West.
The Airlink bus 748 makes a few more stops but all in it is a quick convienent way to get from the airport to Dublin's center.

Take the 16A bus to O'Connell Street. It drops you right next to the spire and was a little quicker than the guide book made out. About 30-40 minutes.

It was only 1.6euros, the Airlink buses cost nearly 5euros are aren't much quicker!

There are several ways of getting from/to Dublin Airport:

Taxi
Turn right outside the arrivals hall for the taxi rank. A ride to the city centre takes about 30mins and costs EUR20 approx.
Aircoach
This brightly blue coach takes you to the city centre in about 40mins and serves the bigger hotels outside the centre (Jury's, Bewley's,...) as well. Single tickets cost EUR6, but for EUR10 you get a return ticket that can be used at any time. The stops in the city are printed on the back of your ticket.
Airlink (bus 747/748)
For 1 euro less (EUR5) and about 10mins more, the green and yellow Airlink takes you to Dublin city centre. This bus makes more stops and only goes as far as the centre and Heuston Station.
Other buses
There are also regular buses running between the airport and the centre. Bus fares are not more than EUR2 but the bus stops virtually everywhere, so it will take you about 1.5hrs (not to mention being stuck in traffic...).