We know very little.

The main problem is that the Irish heroic stories were written down by an educated monastic elite - that is, by Christians, not pagans. Beyond some etchings on stones, there was no literary pagan Irish culture. Irish paganism was not even discussed in anything close to detail by outsiders.

The question is whether the Irish legends represent genuine pre-Christian belief or are just the product of monks who, for whoever reason, felt the urge to write these strange and wondrous stories. Undoubtedly, there is some kernel of pagan belief in the stories, but the extent of this is not known. For example, Lugh is attested as a Celtic god in Gaul as Lugus, and probably was considered a deity by the pagan Irish. However, it has been pointed out that one of his famous episodes, Lugh killing Balor, has strong parallels to the story of David and the Goliath, a story obviously well known by monks. Thus, how much Christian belief was interpolated into the pagan myths? How much of it was written down? How much of it was it still believed and transmitted by a population that readily and eagerly accepted Christianity?

The sad reality is that while it would be lovely to think that the weird and wonderful stories written in Old and Middle Irish were the genuine beliefs and myths of the pagan Gaels they probably weren't. We know virtually nothing of their religion, everything we do have is tricky to separate from the much better attested Christian tradition.