So according to my understanding so far: Contemporary documentary sources report that ancient (pre-Roman and Roman age) Celtic peoples decorated their bodies in blue, both as tattoos and as paint. Some archaeological finds confirm the existence of these blue tattoos.
So what kind of pigment were the Celts using to get this blue color? Was it something native to their own region(s) or were they obtaining it through trade? And what kind of shade was produced by that pigment?
Woad is the traditional answer. A plant that is native to Eurasia and cultivated as a blue dye. However, woad is caustic, and can't be used as a tattoo pigment. Caesar describes the Celts body art as vitrum, the word for glass. Some scholars argue it was a copper or iron based dye, similar to the glazes mixed into Roman glassware to color it.
I have found no evidence that the Celts actually tattooed themselves. Body paint is compelling, and well recorded by Caesar and Tacitus (speaking about Germanic tribes, not Celts), but permanent body art always seems to be an assumption driven by the latter. I've been avidly pursuing the idea of historic Celtic tattoos for my own use, but can find no classicak evidence for it. Let me know if you've got a good source.