Ireland has two official languages, English and Irish (or "Gaeilge" as it is commonly known). Road signs, street names, public bathroom facilities etc may show names in both languages. Gaeilge is the first language of areas of the Gaeltacht in western 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)

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 = May you succeed on the road (Good Luck)

Slán (Slawn) = Goodbye

Sláinte! (Slawn-cha) = Health! (Cheers!) 

Amadán = Eejit = Idiot. 

Glic (Glick) = Cute, Clever, Smartass.

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?".

Just a note on this use of ( sceal ) most people in ireland just say '' WHATS THE STORY '' in asking you what your up to or doing  in the west of ireland it would be used in the irish form but not generally in the south .

Important Sporting Phrases:

Mumhan Abú = Go on Munster.

Dún Abú = Up Down

Rugbaí Beó = Live Rugby

Páirc Thomond = Thomond Park

Also, check out the Irish Slang section for more information on language use.