www.irishrail.ie will give you train times and fares. There are no trains to Dingle itself, but you could get the train from Dublin Heuston station to Killarney, then the local bus 275 to Dingle (see below for bus link). Train journey takes around 3.5 hours. Adult one-way is 33 euros. www.buseirann.ie will give you bus times and fares. If you want to travel by bus the whole way then the best option seems to be the Expressway 12 from Dublin to Killarney, then the Expressway 13 to Killarney, then local bus 275 to Dingle. You'll need to check individual timetables on the site to work out travel time/connections. Online adult one-way fare is 23.40 euro. A combination of train plus local bus (or taxi, if you have the money) seems the best option time- and comfort-wise.
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