Vist the Guiness Factory, the Jail (bit of a weird one, but hey, just try it), city walk to take in the sights, including the Temple Bar area, the city park, the fantastic shops -- two main shopping centres featuring both designer and high street names and of course the various statues, including that of the supposedly first ever prostitute, Molly Malone.
Quick Tips:
Vist the Guiness Factory -- even if you are not into the black stuff yourself -- the history of this beverage is extremely interesting and it's a good place to visit if the weather isn't fantastic (it's Dublin not Dubia remember). Not only do you get the reward of a free drink of the black stuff at the end of it, but you also get one of the best views in the city from the top of the brewery, where on a clear day you can see the beaches and the sea!
Best Way To Get Around:
To 'do' the city centre, do a combination of walking, shopping, walking, drinking, walking, eating, etc.
For the Guiness factory, you will need a head for heights, but you'll get a reward at the end of it!
Try one of the organised tours which range from the sublime to the rediculous.