Read all about how to claim your VAT tax refund at http://www.ricksteves.com/travel-tips/money/vat-refunds.
You can receive a refund one of two ways:
1. For the tourist, reclaiming a VAT is a fairly straightforward process. The typical scenario is to get some form of documentation when you make a purchase, stipulating the amount of refund due. You then show these documents to customs officials upon leaving the country to claim your refund. Most countries specify a minimum amount you must spend in a particular shop to claim a refund. (See chart below.)
2. Some shops in Europe participate in the “Tax-Free Shopping Program.” At these stores when you make a purchase and show your passport you will automatically be issued a refund check showing the amount of refund owed to you. Then, when you leave the country you will show your proof of purchase (receipt) to customs and they will stamp your check(s), which you can then cash at the appropriate desk before you catch your plane, or if you choose you can have your refund mailed to you.
Keep in mind these important facts as well:
Most European countries (Ireland has no minimum) have a minimum purchase requirement (per purchase in most cases) that needs to be met in order to receive a refund.
If you fail to get your VAT forms and/or checks stamped by customs before you leave Europe you will probably not be able to get your refund.
If you get your VAT forms and/or checks stamped before you leave but are unable to submit the paperwork, then and there, you can submit them through the appropriate country consulate in the U.S. once you get home. But, this involves even more paperwork so make sure to allow you enough time before leaving the country to claim your VAT refund.