I would suggest going to your city/ward office and asking what they require to get married first. You can go to immigration and ask questions first, but you need to be married in order to apply for a spouse visa anyhow. So get married.
I'm American, not Irish, but you'll probably have to go to your embassy and get a certificate of eligibility (form proving you're not married in your home country). That's all I got from the American embassy. If the Irish Embassy is anything like the American embassy in Roppongi, they're not going to bother answering any questions for you.
You use the certificate of eligibility to get married at your city/ward office along with whatever forms they give you. You might be required to provide some other documents such as a birth certificate.
Get married. I did it in about 30 minutes without my husband. So romantic...
Then go to immigration, they'll give you a bunch of stuff to fill out and a list of all the forms you have to provide as well. It's better just to ask there, because as far as I can tell everyone's case by case, and while I had to provide X, Y, Z, you might have to do a few things different. I'm not sure. In any case though, immigration is responsible for your visa, so going there and asking is really the best, if not the *only* thing to do.