• by plane : you can take expensive company like Air France or British Airways but two Irish companies offers very good deal with ticket from 1€ from the most european capital. Ryanair (the cheapest) and Aer Lingus. There is also Aer Arran which offers some interesting destination
• by ferry : from france, Great Britain you can choose Irish ferry , Brittany ferry and Celtic link and from Great Britain Stena Line

To move all around Ireland you have several type of transport :

• car : you can use your car but be careful because you have to drive at left ! the road is generally not very large except motorway around dublin.
• bus : Eirean bus offers lot of destination with a good price. It's a good way to travel between big city. Private company (travel tour) organize some very interesting trip in different area of Ireland (go to tourist centre in each city to have more information).
• Train : train is not very interesting because it's very extensive and there is not enough destination (irish rails)

• le guide du routard
  
• wikipedia