Hi June,
It's nice to hear that you are helping your neighbour with her ancestry. This page on
Irish Genealogy Resources is a good starting point, I would say.
In 1864 civil registration was introduced in Ireland, which is when we started seeing the formal registration of births, marriages, adoptions, and deaths. These records have been kept at the
General Register Office of Ireland (GRO), through the Irish Genealogy website, to this day.
I would also recommend that you check out these pages, given that you have mentioned Kildare, Offaly, and Dublin. For Kildare,
this page may prove useful to you. For Offaly,
this page may prove useful to you. For Dublin, you can check out
this page and
this page.
Regards,
Eoin