There are four ways of reaching UL: Car, Train, Plane and Sea.
If travelling by car, please refer to this map of the Limerick area and this one of the campus. The Informatics building is between points 4 and 5 on the latter.
By train you should travel to Limerick's Colbert Station (see here for a timetable) and then take a taxi to the University. The latter should cost £4 to £5. You can also take a bus but not from the station itself. Here is the timetable.
By plane you have a choice of two airports. Shannon Airport is 15 miles away while Dublin Airport is 120 miles. Shannon offers direct flights to Chicago, New York, Paris, London Stansted, London Heathrow, London Gatwick, Dublin and a number of other destinations. Dublin offers a much wider choice of routes, possibly at lower cost.
Your attention is drawn to the fact that Ryanair offers a range of flights to Dublin while Virgin Express fly to Shannon. Flights with these carriers may be much less expensive than those provided by other airlines but you have to book directly with them rather than working through a travel agent. If travelling partly by a scheduled airline and partly by one of these airlines, you may not be able to check your luggage through from your point of departure to you final destination.
When arriving at Shannon, take a taxi to the University. This will cost about £22 and will take less than one hour (half an hour if there is no traffic). You can also hire a car and drive yourself. Finally, you can take an hourly bus into Limerick (costing about £3.50) and then another bus (from another street about five minutes walk away) to the University. This is obviously inconvenient with luggage but we can provide more detailed information on request.
When arriving at Dublin, you can take a bus from the terminal building direct to Heuston Station and then a train to Limerick, mostly changing at Limerick Junction. This journey will take a minimum of three and a half hours. You can also pick up a hire car at the airport and drive. This will also take about three and a half hours.
If you are considering hiring a car for the duration of your stay in Ireland, bear in mind that a fly-drive combining a flight and car hire may be considerably less expensive.
One way of experimenting with different flight schedules and fares is to use Travelocity.
Finally, Ireland may be reached by sea from France, Spain and UK. This is only worth considering if you plan to bring your own vehicle. The principal ferry routes are Cork-Santander, Cork-Swansea, Cork-Roscoff, Dublin-Liverpool, Dun Laoghaire-Anglesey, Larne-Stranraer, Rosslare-Pembroke and Rosslare-Fishguard.