At the Dublin Tourist Information Centre, I purchased a 1-day Dublin Rambler bus ticket for 6 Euros. On the website, it is advertised as a way to travel hassle-free through the city. It does not activate until the first time that you use it. After that, it is good for the amount of time on the ticket (in my case, 24 hours).
I don't know if I actually saved money with the ticket. However, it was worth the peace-of-mind of not worrying about paying the driver the correct amount of change for each ride. Instead, I merely had to swipe the card at the front of the bus.
Take advantage of the Tourism offices throughout the city (and throughout the country)! You know, the offices with the little 'i' hanging outside. You will get free maps, calls made on your behalf, advice on activities and costs, copies of train and bus schedules with all the help you need re; transportation whatever the method, and more. This is free & in my experience these folks were beyond helpful and friendly! They helped me have a successful trip and an enormously wonderful experience while in beautiful Ireland!