I think that with a 'natural' belief system you don't need a pantheon of gods, each with their stories.
You just wonder at the sun and moon and stars, you feel there's something special about high places, deep pools, dark forests. You wonder what all the different plants and animals are there for, you're baffled by the mysteries of birth and sex and death, you fear the dark and the winter, and you give thanks for warmth and light and summer.
You feel that you don't understand much of what happens in the world around you, and you try to form relationships with the invisible forces that control it by making sacrifices to those forces and asking favours of them. you respected the knowledge and wisdom of the old, and you remembered the ancestors, who gradually grew into legendary and semi-divine beings.
It didn't matter that such basic beliefs didn't hang together philosophically particularly well: you just had an unreflecting acceptance that most of what happened was a bit of a mystery. But you trusted those people in the community who appeared to understand the mysteries of life better than you - the shamans.
I think these shamans genuinely believed that strong drink, drugs, dreams and various meditation techniques put them in touch with the 'Otherworld'. I also think that since they got a reasonably good living from this, and didn't have to work like other people, they used a few cheap tricks to fool the people (like stage magicians do today, for example, in order to convince everyone that were not to be messed with.
The big question, I think, is whether natural pagan Anglo-Saxon beliefs were ever formalised into some kind of system - were pagan priests trained, elected, appointed, as were druids before them, or Christian priests after them? And if so, by whom? Was there ever a canon of dogma which was familiar to every pagan priest north, south, west and east? Did they have a particular way of speaking, or dressing, and was there (literally) a hierarchy?
I'm beginning to suspect that such a formal hierarchy DID begin to evolve before the coming of Christianity, and that it was inspired by the Roman system. By what mechanism, for example, was the pagan seven-day week introduced? It may also have been helped along by a 'folk memory' of druidry. Perhaps the Celtic Christian 'back-and-front' tonsure was a continuation of previous druidic practice.
all just idle speculation, of course, but what do folks think?