http://www.groireland.ie/getting_married.htm
The above link should answer all of your questions.
Step 1 would be to fill out the Notice of Intent to Marry form and send it to the registrar where you want to marry. They will then have you and your fiance come in for an appointment. Prior to the appointment you must show proof that you were resident in the district for at least 7 days. If you live in Dublin and want to marry in Dublin, you can take household bills, etc. You will need your ID, birth certificate, and divorce decrees if either of you have ever been married before. You can then set a date to marry, but must wait at least 90 days from the time the registrar received your notice of intent. Just to forwarn you, the Dublin registrar is very busy and there have been couples waiting 6 months or more for a date to actually marry.
As far as you both being not from Ireland, there is nothing on the site that specifically addresses this. I'm not sure if they ask for proof of being in Ireland legally, or if they even bother. But, I don't think there is any added paperwork required.
