I'm new to genealogy, so hope you'll be patient with me ...

I've just found that I have some Irish ancestry, my maternal great~great~grandmother was Maria Nesbitt, born in Leitrim, c 1847 (married Joseph Robinson), and my great~great~great~grandfather was Henry Nesbitt also born in Leitrim, c 1821, who married another lady named Maria.
I just wondered if you can advise me as to the best places to try to find records to trace further back?
Many thanks for your time and help,
Pippi