Phone numbers in Ireland are broken into 2 parts:-
1. The S.T.D. or area code e.g. (01), (090) etc.
2. Phone number.

The S.T.D. code is only required if you are calling a number in a different area.

If you are calling from outside of the Republic of Ireland you first need to dial an international access code usually denoted by a "+" typically 00 (check with your service provider) followed by the country code of 353, then you drop the first 0 of the S.T.D. code and finally the phone number.

Example
From within Ireland
(090)-6485406

From outside Ireland
+353-90-6485406 (again the + is usually 00)

Selection of Area Codes in Ireland
01 Dublin
021 Cork
061 Limerick
091 Galway
071 Sligo
042 Dundalk
090 Athlone