Shannon airport is Limerick's local airport, direct flights to Europe are available but fewer destinations than in the past as Ryanair have had a long running battle with the airport authority over landing fees here. Air lingus pulled out for a time and now only operate to a couple of places. Jan '11 lists only 15 destinations for scheduled flights.
Transatlantic flights are still available,however from Delta and Continental to Newark & JFK.
Check out more info at by shannon page. As airports go it has quite an interesting history.
The easiest way to get there from abroad is by flying into Shannon. Thomas Cook for example offers non-stop flights to Shannon from Frankfurt. Other posibilities are flying into Dublin and then taking the train or bus to Limerick. A friend of mine did the first mentioned, however she said she regretted it! So I guess it's better and more comfortable to take the bus, even though the journey takes a little longer thus.
Shannon International airport, the second largest airport in Ireland, after Dublin, is very close to the city. You can fly into Shannon, and then catch a bus into town. Depending on where you're flying in from, you may get a better deal if you fly into Shannon instead of Dublin.
Shannon Airport really should be called Limerick Airport, considering Limerick is the nearest city to it! ;-)
It's a big & dull-looking airport, mainly servicing North America, UK & Europe.