U.S. citizens may enter Ireland without a visa and remain in the country as a tourist for a maximum of 90 days per trip. If you wish to stay longer than 90 days, you need to seek permission to remain in the country.
Residency in Ireland is not difficult to obtain, but requires a minimum annual stay in the country. Like many countries in Europe, Ireland grants residency to foreigners who can prove they can take care of themselves (that is, pay their own bills and not be a burden on the state).
Residency in Ireland can lead to a second passport and dual citizenship in this country.