The Proto-Indo-Europeans were classically polytheistic, worshiping a number of gods and goddesses. We can reconstruct a number of these, but not all. They had myths, although we can only reconstruct a few, and those not in detail. And ritual, especially its correct performance, was extremely important. I talk about these on other pages, so here I'd like to concentrate on two principles. They interact with each other, but I'll try to explain them separately.
The first is what I call the ghosti-principle. *ghostis is a PIE word which means "one with whom one has a reciprocal obligation of hospitality." Our words "guest" and "host" both come from this word, and that is just what the ghosti-principle implies. There is an interaction among people, and between people and the gods, according to the laws of hospitality. Society is bound together by an exchange of gifts, by acting as guest on one occasion and host on another. In the same way, we are bound to the gods through the giving of gifts and the receiving of blessings. This is the origin of the Indo-European version of sacrifice. When one was performed, some of the animal was burned to go to the gods, and then the people who offered it ate the rest, which was most of the meat. The sacrifice was thus a shared meal, in which the people served as hosts and the gods as guests. Since the gods know the rules of hospitality, they would then be obligated to serve as hosts on another occasion, and they would do so by granting us favors. Although some see this as a cold contractual exchange, it is through this exchange that a relationship is created between the gods and us, bind us closely to them in a shared society.
The second is the *Xártus, which is the pattern of the universe. This word comes from the root *xar- (H2-), meaning "to fit together in an appropriate and aesthetically pleasing way." Both linguistically and ideologically Xártus is the root of the Vedic ṛta, and the concept is similar as well to the Germanic wyrd. The Xártus is the pattern of the cosmos, but not one that’s imposed from without. Instead it grows from the cosmos itself.
The Proto-Indo-Europeans saw the cosmos as centered around a tree and surrounded by water, which also rose up through a well to feed the tree. The tree was the cosmos itself, an ordered arrangement of things and actions, and the water was chaos, disorder. Notice that order is fed by disorder. Left to itself, order, like an unwatered tree, becomes brittle and dead. An influx of chaos is vital to its life. Chaos is dangerous and not capable of supporting life on its own, however, and only becomes meaningful when it is drawn into Order. It is through this interaction (a kind of ghosti-relationship) that the universe can continue to exist.
Order gifts chaos in another way. Things passing out of existence, not only as in living things dying, but even as each moment passing away, are going from order into disorder. If cosmos is seen as the tree, then its dying bits are fruits or nuts. This imagery is found clearly in the Norse cosmology, in which drops of honeydew fall into the surrounding waters. In this way again chaos and cosmos are joined together into a relationship. Chaos gifts order, and order gifts chaos.
If the cosmos is a tree, then its branches form a pattern, which is the Xártus. Notice a number of things. First, the pattern forms itself out of the growth of the tree itself – as the cosmos grows, and actions and things arise and are added to the cosmos, the pattern of the branches changes. The Xártus therefore arises from the cosmos, rather than from outside it.
Note as well that although the cosmos grows the Xártus, the Xártus has an affect on the cosmos. The growth of the tree is not completely free; branches can’t grow from anywhere, and they can’t grow in any way they wish. It may be said that the Xártus impels but does not compel.
We form our lives within the organizing Xártus, and then our lives, like all things that happen in the cosmos, are fed into the Xártus. The things we do, as they pass away, and eventually we ourselves, also fall into the waters of chaos. Eventually, however, like the water from the well, all that we have given to chaos returns to cosmos, transformed first in the waters, and then by the tree. Like the tree, we have been fed by chaos, and we then feed chaos in turn.
In both the ghosti-principle and the functioning of the Xártus, we see the working of the central ideology of the Proto-Indo-Europeans, that of reciprocity. This is at the root of our relationship with other people and with the gods, and at the nature of the cosmos. It is impossible to understand PIE religion without understanding reciprocity.
I have a page of unorganized thoughts about the Xártus here.