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The first thing you need to do is interview all your family members and get whatever info they have - names, dates, places, family traditions, etc. Get it on tape or 3x5 cards, whatever, just you can refer to it easily, as you need to. You can keep records on paper or on a genealogy program for your computer. The 2nd thing I would tell you to do would be to contact the nearest LDS Family History library. They are open to the public for genealogy research, are well versed in the research and are of a valuable help in that area.
I also research the Maloy/Malloy surname of IRL (prob County Mayo) also of Kingston, Ontario, Canada, Oswego Co, NY, Oneida Co, NY, Montcalm Co, MI. I have begun just a tad of some Malloy research in RI. If we can be of help to each other on the Maloy/Malloy surname, I am always happy to exchange data. You may contact me at: email@example.com Bunny