To publish a book in Ireland, a complete manuscript or well-rounded summary of a story idea is needed. It is helpful to hire a proofreader or freelance copy editor to review the manuscript or summary before contacting anyone in the publishing industry.
Research Ireland's publishing houses to find the one that caters to the kind of book you're seeking to publish. There are many publishing houses in Ireland, many of which are listed on the Irish Book Publishers' Association website. They're specialized and are approached often with ideas, so know who and what you're looking for.
When you've found a publisher who you like, do some research and find out how she prefers to be contacted with a potential book deal. Some prefer the full manuscript, others only read summaries and some want to be contacted by a literary agent, not the writer.
If you're having difficulty getting in touch with publishers directly, get a literary agent who knows and understands the Irish publishing business. To find a literary agent in Ireland, consult Writers.net, which has a list of literary agencies and can make a proper recommendation. An agent will know how and where to market your writing, and will help you navigate the world of publishing.
Another option, which is particularly useful for short story writers and poets, is to submit your manuscripts or partial manuscripts for awards or literary publications. The Fish Short Story Prize, hosted by Fish Publishing in the West of Ireland, offers awards and publication for poetry and short stories. The Stinging Fly, in Dublin 8, is a magazine dedicated to publishing short works from Irish and international writers.