The Irish have emigrated all over the world in the last 250 years. Many generations later, it can be very difficult for their families to trace their roots back to a specific location. They may only have a surname, or perhaps a local name or two passed through the centuries. Many of the official Irish records were destroyed in a fire around 1920, which makes a genealogical search even more difficult. But don't despair.
Help is at hand.
If you have a surname, you may get help from books on Irish surnames. Many names are specific to a few counties. For example, the Cribbin surname has very specific links to a small town in county Mayo. Other names have clear links with the South of the Country because of their Norman origin. This kind of information is a good start to limiting your search area.