Driving is the best way to visit Ireland if you want to see the landscapes, coast, and small towns and villages that make the country so famous.
While train links from Dublin to other cities in Ireland are good, rail connections and public transportation are not extensive outside of major cities.
Driving allows you to explore more of the off-the-beaten-path areas that make Ireland so well-known for its natural beauty.
Keep in mind that driving in Ireland is done on the left side of the road, and most cars for hire in Ireland will have a manual transmission (stick shift). You can get a car with an automatic transmission, but there are fewer of them available and they usually cost more.
Dublin airport offers a car hire option through several large international companies. There is also car hire at Cork airport, car hire at Shannon airport, and at other airports throughout the country.