Galway is a major tourist destination in the west of Ireland, on picturesque Galway Bay. The most direct route to Galway from outside Ireland is Shannon Airport, in County Clare. There is a direct bus connection from Shannon airport to Galway city centre. Buses depart from the airport arrival gate, and return to the airport at the departure gate. It cannot be simpler. Bus tickets can be purchased online or at the airport, at well marked locations. Again, this is the most direct way to travel from Shannon airport to Galway centre. The cost is 9.50 Euros one way. Of course, prices might rise slightly during the summer, but that is not reflected now. Student rates are less. TripAdvisor also recommends the bus rather than the train from Shannon to Galway given that buses depart and arrive at the airport's arrival and departure gates. Staff personnel at Shannon Airport will be polite and willing to assist.
The link to Bus Eireann, Ireland's public bus service, is: http://www.buseireann.ie/inner.php?id=251
Car rentals are also available at Shannon airport (Hertz, etc.). A few people could share a vehicle, for example. The problem with this might be parking in Galway, which can be difficult during the summer. Hotels will have parking arrangements with the public car parks which will offer reduced rates for their residents. Some B & Bs will also provide parking, if one elects to stay in B & B.
If one flies to Dublin, then rail is the way to travel across to Dublin from Heuston Station. The cost one way is 36.50 Euros, and student rates are less. The link to Irish rail is:
Taxis are in abundance in Galway. They can be ordered from the hotel desk, or engaged on the roads. The fare to the National University of Ireland Galway (NUIG) campus from Jury's Inn (Galway centre) is very reasonable as it is a short ride. Some taxis are small vans, so many can share a taxi. The hotel folks are very accommodating and might be able to order larger taxis the night before. In addition, the taxi drivers in Galway tend to be very polite and talkative.
One can walk from Jury's Inn to NUIG, this would take a maximum of 25 minutes at a leisurely pace.