Flight
If you are flying from the United States the most common (and usually least expensive) airport to fly into is Dublin - DUB. Limerick is about a 2 hour drive from the Dublin Airport. Once you arrive in Dublin you can either rent a car or take a shuttle bus to Limerick. There are shuttle buses that leave right outside the airport that go straight into downtown Limerick.
Flight
The closest airport to fly into is the Shannon airport - SNN. The Shannon airport is about a 30 minute drive from downtown Limerick. Once you arrive in Shannon you can either rent a car, take a shuttle bus or taxi from the airport to downtown Limerick.
Travel Note
There are multiple different bus services that can get you from either airport to Limerick. We usually use the Bus Eireann company. They operate shuttle buses from both Shannon and Dublin airports to Limerick. The Limerick Bus station is the most centrally located. Follow the link to find out more information about departure times and bus services.