To have a realistic chance of finding anything significant,
the minimum information generally required is your ancestors'
county of origin in Ireland. If you know the precise location,
so much the better. A word of caution: Irish counties are generally
larger and much more populous than North American counties.
From this page you can look at some of the sources relevant
to all counties, subdivided by province. Comprehensive and up-to-date
information can be found in Ancestor search.
In general the following information is listed for each county:
Census returns and substitutes