How should someone set up an altar to the Celtic gods in a recon way?
Here’s the thing about that: you don’t. Historically speaking, the closest thing a person would have to an altar or a shrine would be the hearth. There was no set place in the home where one would go to honor the gods.
To approach the issue from a different angle, (although it’s one that, to my knowledge, applies only to Irish polytheism, specifically), the nature of the relationship between the gods and the people was not one where the humans and the gods are on seperate planes or in seperate realms; the gods were manifold and everywhere, and the nature of the people’s worship was not one of subjection, but of contractual obligation. The gods, who were defeated in battle by humans, moved under the sidhe—the fairy-mounds, as it were—and agreed to let the crops grow and the livestock live in return for offerings of food and milk and things of that nature. Offerings of food, milk, grain, fruit, etc., would be left outside in the woods, or burned, or buried. Weapons and armor and sometimes entire chariots were sunk in lakes and rivers.
However, that is not always adequate in the context of a modern practitioner of the religion. It’s not always practical, and the concept of the contract between humans and gods is inapplicable, especially if you don’t live in Ireland, at least in my opinion. The nature of the relationship between the practitioner and the gods is fudamentally different than it should be if one were truly reconstructing the practice. One of the results of that paradigm shift is that many Celtic polytheists, require some kind of workspace for our practice. I take it you’re in a similar place, hence the question. In that light, what you do for an altar is almost entirely up to you, so long as you don’t do anything that’s blatantly in conflict with the way the Irish gods have been worked with historically. It should be a tool for the revitalization of the religion, not a reinventing of the religion. So that means that if, for example, you make an offering of buttered bread and milk to a Celtic deity, (which is always a good offering to start out with, by the way, at least with Gaelic deities), and now it’s been a few hours, or overnight, or however long you see fit to leave it there, you wouldn’t eat it yourself, because that would be disrespectful and, according to legend, very unhealthy. You’d also want to avoid throwing it away, but that’s less important and more difficult depending on your situation. Things of that nature still apply.
Bolded the important bits.I hope I actually answered your question somewhere in that throng of tangents.