I am very new at tracing my family tree and I could use some help in finding

Martin Conroy, coming from Ireland in approx 1885 to Massachusetts.
His birthday is May 1855.
I do find one listing, but I do not know how to know if it is him, or how to locate his parents to go back farther.

I am also looking for his wife,
Mary Moroney, also coming from Ireland, not sure of year, but born in 1863.
Children are
Mary C Conroy
Nellie A Conroy
Margaret H conroy


They were not married when coming over but I can not locate a marriage license licence in the US. In the US, they lived in Salem, Massachusetts.

I guess I am really confused as to how to search when dealing with countries other then the USA and would appreciate any help or hints to find the history or a way to go farther back in Ireland.
Any help would be greatly appreciated.
Thanks