Getting to their I think you would have to go via Copenhagen, I don't think there are any flights from anywhere else to Greenland apart from maybe Iceland which itself isn't directly accessible from Ireland.
I'm afraid I have no idea of the costs up there but given the remoteness I would imagine they are astronomical ... not a cheap holiday I would say.
Any particular reason for Greenland ? - if it's artic landscape/outdoors stuff you're looking for why not try Iceland or the far north of Norway/Sweden/Finland... while none of these places are cheap they would be a lot more accessible and have more facilities etc. for tourism.