So you've just landed in Ireland. You might have already found a place to stay, a house, an apartment, a hotel or even a student hall. But the single most important thing to do is to get a PPS number.
The PPS (personal public service) number is the equivalent of a social security number. You can't get payed or rent a house without one. It's pretty darn important and this is the first thing you should do when you move to Ireland. In order to get one, you ned a valid means of Identification and a proof of residence. A valid Irish phone number as well as possible proof of employment could come in handy.
Since you are most probably a non-Irish national, a valid passport is more than enough. My guess is that a national ID or a drivers licence could suffice, but I wouldn't bet on it.
Proof of residence:
I said that you need a PPS number in order to rent a house, and now that you need a house to get a PPS number. Puzzled? You shouldn't be.
As you will find out, the Irish are relaxed about things. Laws are there to get bent a bit (except parking violations). So... you can get a letter from your hotel manager, saying that you live there, or if you found a place to rent, a letter from the owner or the real estate agent. Just ask. They are quite used to the letter referencing system, so they will most probably be happy to oblige.
Irish phone number:
If you don't have a landline, a mobile phone number is perfectly OK. You can get a free SIM from every major mobile telephony operator (O2, 3, Vodafone, Meteor). O2 seems to be the most popular. A walk in Patrick Street, Cork will let you find these operators.
Proof of employment:
I started a Ph.D. so I had a letter prepared for me by the Department administration office. This letter includes my name, Passport number, address of residence, work address, the estimated duration of employment (Ph.D.: four years), and the annual salary.
When you gather the necessary paperwork, you should head for the social welfare office.
View Cork Social welfare office in a larger map
Head here early-ish, or you might need up to an hour or more of waiting. If your documents are in order, you will be notified of your PPS number via mail in up to two weeks time. If you are in a hurry, you might be able to obtain your PPS number if you phone the welfare office.