What is the quickest and most efficient way to apply for her citizenship?

Generally, the process is rather straightforward: after receiving a Certificate of Marriage, you fill out several forms (I-130, I-485, G-325, I-864, I-765, I-131) and send them to USCIS. The forms and the instructions are posted at uscis.gov/forms. If your paperwork is done right, in a couple of weeks you receive a Notice acknowledging submission of the forms; a bit later - an invitation to the fingerprinting center; and, in a couple of months - a summons to an interview at 26 Federal Plaza. If you pass the interview, your wife would get a temporary green card, good for 2 years. If you marriage survives for 1.5 years, you will file papers asking the government to give your wife a 10-year green card and to remove the condition tying her status of U.S. permanent resident to continued validity of your marriage (after that, she can divorce you and still keep her green card). 3 years after becoming a permanent resident, she will be able to apply for U.S. citizenship (but, if she divorces you, she will have to wait 2 years longer before applying for citizenship). In your case, there is wrinkle. When your fiancee enters the U.S., she will be asked to state the purpose of her visit. If she comes on a tourist visa or a visa waiver (available to her as to a citizen of Ireland), she must state that she has no intention of immigrating to the U.S. Should she admit that she comes to get married and later apply for a green card, the immigration inspector must turn her around and send her back to Ireland. If she lies and gains entry, when you file the immigrant petition and the application for a green card, USCIS will say that she entered the U.S. under false pretenses, i.e. committed a visa fraud. It might make sense to apply for a fiancee visa, K-1. The process is simple; the form and instructions are at uscis.gov. It costs $340 to file; and USCIS will take 5-6 months to process it. If you have reasons not to follow the K-1 visa procedure, talk to an immigration attorney about the alternative solutions.