No matter under what circumstances you are applying for the Irish Citizenship, the real first document you will receive as an Irish citizenship will be a certificate attesting your new nationality. With this certificate, you can apply for your Irish passport and also for other official documents.
If you obtained your citizenship through decent, your certificate of citizenship will be issued right after your foreign birth registration will be accepted by the competent office. A post nupcial citizenship will make you able to get your certificate of citizenship once your papers will be verified by the Department of Justice. In cases of Irish citizenship by naturalization, on the other hand, the document is obtained in a Naturalization Ceremony.