A reconstructionist, often referred to by the abbreviated term “recon”, is someone who wishes to emanate and practice their religion in a manner they best understand the ancients of a particular culture practiced it.
What we often find while doing research into these paths is the common goal of recreating the pre-Christian religions in the modern world. While there is much information to glean what one needs, as far as religious practices go, there are definite gaps, so most reconstructionists move forward to create a fill in that seems most logical and fits in with how other rituals or practices are performed.
The most common paths of reconstructionists in Western paganism are the Hellenic (Greek), Roman, Celtic, and Asatru (Norse). These people not only worship the Gods of their respective chosen religion, but they also pull on the information in written lore and histories to glean the worldview and way of behaving to permeate the whole of their lives. Of course, there are many other reconstructionist paths, Egyptian, Canaanite, Baltic, Slavic; there are even Christian and Jewish reconstructionism.
Hellenic reconstructionists gather information from the wealth of written works by the likes of Homer, Hesiod, Orpheus, and Herodotus, etc. The literature provides the stories and myths of the God/esses, how They interacted with humans, hymns and prayers used to call upon said deities.
Celtic reconstructionists take their practice cues from the archaeological record, oral tradition and folklore preserved by Christian monks who recorded local legends. Celtic recon includes a wide variety of practices and Deities native to the various Celtic regions of Western Europe. There are many sub-traditions as well as more pan-Celtic traditions that incorporate deities and practices from many different Celtic communities. We also find druids in Celtic recon, although not necessarily every druid group can be categorized as reconstructionist.
Also known as Heathens, Asatruars and Odinists, Norse reconstructionists attempt to recreate the pre-Christian religious and daily practices of Northern European peoples. They use the information found in the Eddas and Sagas. There is a focus in Asatru on honoring the ancestors as well as the gods.