Dublin offers many Cheap Hostels. If you're ok with sharing a room with other people you may find a bed for as low as 9 euros. For a private room be ready to spare 12 euros and up.
The good thing about the hostels is that they're sort of sociable accommodation, as well as low budget oriented, however do remember that you are sharing room, bathroom, lounge and sometimes even kitchen.
There are many web sites offering price compassing of the hostels in Dublin. Many of them are located in city center which gives easy access to the bus stops and the  city attractions.

Another alternative for finding accommodation in Dublin is Couch Surfing.