If you are just interested in the sound of Dublin English and the main features then the quickest was is to consult the module Themes and then All sound files together with the Glossary which explains the main features of present-day Dublin English
If you are interested in the history of Dublin English, you should start with the module Overview and branch out from there.
If you are interested in the most recent developments in Dublin English and especially in the question of parallels between Dublin and other major anglophone cities, then you should go to the module Most recent changes.
If you are interested in theoretical issues surrounding language variation and change in urban complexes, you should go to the modules Supraregionalisation, Dissociation and Implicational scales. Also consult the module Most recent changes.
If you want to inform yourself about Irish English in general before delving into the details of Dublin English, go to Phonology of Irish English, Terminology and Misconceptions first, then proceed with Overview and move on from there.
For information on other cities in Ireland, you should check out the module on Belfast English and on Derry English, perhaps looking at Ulster English as you proceed.
Otherwise just browse around the site and read and listen to what might interest you.