I could spend a lifetime describing how the Irish ended up in Connecticut. I'm sure we all can think of the basic causes: the Irish Potato Famine and political turmoil. However, it's usually more complicated. Don't forget to look at your ancestor's experience after the United States. It's often reflective of why they immigrated. Not everyone wanted to be an industrial worker in a city.
How do you find records of your Irish ancestors? You can start by reviewing books on Irish genealogy. Tracing Your Irish Ancestors is one of my favorites. It's a good way to familiarize yourself with the basic local sources. Then try to track down the local Catholic church. Many Irish immigrants were Roman Catholic, and their churches, often the oldest RC churches in Connecticut, document their life in great detail. Finally, don't forget immigration and travel records. I finally located my Irish ancestor's birth location on his daughter's passport. An ancestor's naturalization papers may also list that information.