Ireland has two official languages, English and Irish ("Gaeilge" in Irish). Road signs, street names, public bathroom facilities etc may show names in both languages. Irish is the first language of the Gaeltacht regions in Ireland, however, its day to day use in the rest of the country is limited, although you will come across it. Some key words / phrases are:
General
Éire = Irish name for Ireland
Muintir na hÉireann - People of Ireland
Fir = Men (on public restroom signs)
Mná = Women (on public restroom signs)
Place Names
Baile Átha Cliath = Dublin
Corcaigh = Cork
Gaillimh = Galway
Muine Bheag = Bagenalstown (often in Irish on maps)
Laois (Leesh)
Luimneach = Limerick
Port Láirge = Waterford
Neidín (Nedeen) = Kenmare
Cill Áirne = Killarney
Léim an Bhradáin = Leixlip
Greetings
Dia Duit (JEE-a Gwitch) = Hello
Conas atá tú? (CUNN-us a TAW too) = How are you
Go raibh maith agat (GURRA mah agg-utt) = Thank you
Go n'éirí an bóthar leat = That the road may rise with you (Good Luck)
Slán (Slawn) = Goodbye
Sláinte! (Slawn-cha) = Health! (Cheers!)
Amadán = Idiot.
Glic (Glick) = Cute, Clever.
Gabh mó leisceal = (Gow moo leh-schale) Excuse me.
Sin é = (Shin Ay) Thats it.
The English language is also peppered with use of anglified gaelic words and you may come across these. For example, a good night out might have been 'great craic' (pronounced 'crack') or a greeting may be 'whats the craic?'
The Irish word for "story" is 'scéal' (pronounced 'Shkale') so someone looking for information might ask - "What's the sceal with that?".
Important Sporting Phrases:
Múmhan Abú = Go on Munster.
Dún Abú = Up (County) Down
Rugbaí Beó = Live Rugby
Páirc Thomond = Thomond Park
Also, check out the Irish Slang section for more information on language use.