There are approximately 56 different unions (representing almost 800,000 employees) linked to the Irish Congress of Trade Unions.
I am not quite sure which union is appropriate to those in your profession - it may be the Communications Workers Union ([broken link removed]). However, I would recommend getting in touch with the Irish Congress of Trade Unions (ICTU) for advice. (http://www.ictu.ie).
On another note - while you have a constitutional right to join and be a member of a union - your employer does not have to recognise union membership. In addition, they can refuse to negotiate with unions on your behalf regarding employment matters.