Dublin Bus has rambler tickets (1,3,5 day etc) which can save you money if you are going to be jumping on and off buses a lot. They also have a 3 day freedom ticket which also includes tours and the nightlink buses (which may come in handy depending where you are staying)
The private Blue buses are a comfortable and easy way to get from the airport into the heart of the city and beyond. Check if your hotel is on their itinerary and then jump aboard. You can also catch the public 747 bus into the main bus station in the city Busaras. There are also buses that can take you directly from Dublin airport to Belfast, Galway, Cork and other towns without having to go into the city (which can save a lot of time if you don't plan to stay in Dublin)
www.aircoach.ie - Blue Buses
We took the Irish Ferry to Dublin, and then got on the bus at the Port. Make sure you get on this bus as there are a very limited number of taxis and it's a long walk to the nearest bus stop!