Most people fly into Dublin. From there, it's a 4-5 hour journey by train or a 5 to 6-hour trip by bus. When you fly into Cork or Shannon, buses can take you there.
Another option is to fly straight into Kerry AIrport, located between Tralee and Killarney. AerArann has scheduled flights from Dublin and reasonable one-way fares.
Since public transport practically doesn't exist in Kerry, it's a VERY good idea to rent a car whenever you need one.