Advice on finding where an ancestor came from?

Hello. My name is whitney and I live in the U.S. We know my family on my grandfather's side came from Ireland and we are very proud to be Irish descendants. I know my great great great grandfather was named Martin Kelly, born about 1833/1834 in Ireland. We are not sure where in Ireland though. We know we eventually moved to Bridgeport, Connecticut, USA. He married Ellen Elizabeth Dunn. I know she was born in 1830 Limerick, Hibernian, Ireland. At least that's the information I got from ancestry.com. I know once in the US he had a son Martin William Kelly on 14 march 1859. Any advice on how to gather more Information? I know this will be difficult with the many different Kelly families all over Ireland.