Here are some links to some significant research resources for Irish genealogy. While many records have been digitised they have not always been transcribed accurately so to be thorough you should visit local archives, family history centres, graveyards, libraries etc. You cannot do comprehensive genealogical research purely over the Internet and certainly not without spending any money.
Irish Birth, Marriage & Death Records
Irish Genealogy (Free church records provided by Irish Government project)
Census, Wills, Military and other Records
Books, Reference texts
Guides to History
The Plantation of Ulster (BBC)
Mary Lennon and Ros Davies are deserving of high praise for their genealogical resources.