Anyone who has a parent or grandparent born in the Republic of Ireland or Northern Ireland can get an Irish passport by applying to your local embassy or consulate.
You need to have the following :-
1) For the Irish grandparent, birth certificate and marriage license to whoever was the other grandparent of the applicant.
2) For the parent (child of the Irish grandparent) birth certificate and marriage license to your other parent.
3) For you: birth certificate
ALL of the above documents must have complete details that prove the connection. In other words, the birth certificate must show the names, dates of birth and places of birth of both your parents, so that they can be conclusively identified to be the same person mentioned on the marriage license and their own birth certificate. Irish documents seem to include these details automatically, but in the U.S., you may have to contact the Vital Statistics Bureau in the state of birth to get an official copy containing more details.
ALL of the documents must be official, i.e., must bear the raised stamp of the issuing agency.
You have to fill out forms, attach photographs and have it all witnessed, not by a notary public, but by a "clergyman, high school principal, lawyer or bank manager".
It costs about $160 if you are claiming through your parent(s), in addition to the cost of getting copies of the documents. If you are claiming citizenship based on your grandparent(s) then you need to pay $270 for Registration of Foreign Birth.
There's about a one-year backlog in processing applications.