Good morning from Dublin!
Your question is very general and I could probably help you better if I knew what your particular interest is.
I can tell you that in Dublin there is a rent a bike scheme - www.rentabikedublin.com and that here are tours of the city by bike - www.dublinbybike.ie. There are cylcing lanes in parts of the city and suburbs.
If you plan to be out of the capital www.cyclingsafaris.com might help.
If this is not the sort of information you are looking for please get in touch again with a more specific query and I will try to help.
Dublin, Ireland almost 10 years ago