Like Maria and C said there is no problem getting cash at the airport. There are many ATMs at the airport. In fact, there's one right off the Security area in Terminal 1. Make sure you notify your bank of your traveling dates and destinations before you travel. You may want to find out if there's a fee to withdraw cash in Ireland. There's no harm in getting cash from your bank before leaving too. It would probably make you feel better if this is your first time traveling overseas. When I was in Tampa, I had to order foreign currencies a few weeks (2 weeks) in advance. Most banks there do not carry foreign currencies. Here in NYC, there are ample places to exchange for euros. Credit cards - Mastercard and Visa are widely accepted throughout Ireland.
Hi again Kelly, Well the dollar is strong at the moment so maybe get some cash for the first day or two. There are ATMs almost on every street in Dublin and also at the airport so you will have no problem getting cash. Most small towns have banks with ATMs so, even if you plan to travel down the country you'll be fine. Credit cards are accepted everywhere. Visa and Mastercard are most commonly used.
All the airports you are likely to fly into will have ATMs at the exits so as long as your credit card lets you, you should be able to get money immediately. Check with your card company first though as America has such a range of cards you want to make sure you've got one that's going to be ok. Most Visa and Access cards are ok but, as you're already worrying about it, might be worth double checking. Be aware that most places in Europe demand chip and pin number rather than signatures for card transactions. If you haven't been to the Eurozone before, getting some cash before you arrive gives you an opportunity to get used to the euro notes before you arrive tired and jet-lagged. Failing that most post offices and banks will be able to change the money once you're here in Europe (got to say that while I still can!)