Galway is situated on the west coast of Ireland and may be reached by air, ferry, train, bus or car or a combination of these. To help you find the best access route to suit you, please see the following site for further information http://www.discoverireland.ie/
Perhaps the easiest way to get here is to fly to Dublin and then get a connecting flight to Galway. Dublin airport information is at Dublin Airport.
Aer Arann fly 4 times a day from Dublin to Galway airport. See http://www.aerarann.ie for details.
Galway airport offers connections to many of the major British Airports including Luton and Manchester, so connecting from these airports may suit some people. There is also a service to Lorient, so please check the airport web site as new routes are opening up regularly. The link is http://www.galwayairport.com/
Galway airport is just a 15 minute drive from the city & euro 15.00 by taxi.
Another way of getting here is to catch a bus from Dublin airport. You can do this by going to the coach park (follow the signs at the airport) and then catch the CityLink bus or GoBus direct to Galway. Here is a link for the timetable (City Link) http://www.citylink.ie/ and the GoBus link is here (http://www.gobus.ie)
GoBus is direct and its facilities are quite good.
If you would prefer to get here by train, then go from the airport to Heuston Station (not Connolly Station) in Dublin and then catch the train. The bus to catch at Dublin airport is the 748. Details are here: http://www.dublinbus.ie/your_journey/airport_services.asp
The train details from Dublin to Galway are at http://www.irishrail.ie/home/
Alternatively, there are a number of other access points - Shannon airport may suit people coming from the U.S.
Shannon Airport (approx. 1.5 hours by bus/car)
CityLink offer a bus service between Shanon and Galway. Details are at http://www.citylink.ie/timetable-galw2shan.htm