There are layers of complicated issues separating your excellent question from the answers you seek. One of the fundamental problems here is the very use of the word "religion." For someone from a twenty-first-century point of view, that word connotes a formal institution with a hierarchy of professionals administering to faithful adherents who go to a structure (and the institution it represents) for spiritual completion of existence. What existed in pre-conversion societies might be better referred to as "belief systems" because it was often so far removed from what we think of as religion.

Other issues reside in the fact that "pagan religion" refers to hundreds of societies spread over millennia, so arriving at generalities is problematic. In addition, there were certainly differences between urban and rural practices: as cities grew in strength, so did a hierarchy of spiritual professionals, so what they practiced began to come closer to the idea of religion as we conceive it.

Another problem is the lack of clear written texts to determine how people approached their belief system and their idea of spirituality. Those educated few who wrote about belief systems, tended to institutionalize stories and belief, creating what is certainly the wrong impression that their society had a singular, monolithic understanding of the gods and how to approach them.

Ethnographic evidence (which provides an imperfect analogy) lends some insight into how everyday, "regular pagans" viewed supernatural beings, faith, devotion, and the stories about all of that. Folklorists and ethnographers find that in pre-literate societies there is often considerable disagreement about all these aspects of a belief system. Some people believe more than others, but people also disagreed about particulars, and this is typically reflected by contradictory stories, sometimes told by the same individual. People groped for answers, took what was meaningful to them at the moment, and looked past the rest.

In 1981, I spoke with a woman from the country who was living at the time in Dublin. She said that when she was in Dublin she did not believe in banshees, but when she returned to her country home, the belief reestablished itself, and she became a believer. She mused over this and clearly didn't fully understand how that could happen, but that is what she described.

Think about how modern people address the beliefs in ghosts - or UFOs! This is a good opportunity for something of an analogy since it is part of a modern belief system that resides largely outside institutional religion. Everyone is familiar with the idea of ghosts, and most have heard stories about them. When asked whether one actually believes, the answer can be different from moment to moment and in different settings. We approach the idea of these spiritual beings with a certain amount of deference (depending on the individual), and we accomplish all of that without institutional reinforcement of a church, temple, or mosque.

So, to attempt to provide a generalized (and necessarily flawed) answer to your question: people understand the core aspects of their belief system because they grew up with the stories and the folk practices (consider the practice of knocking on wood!) that filled their everyday life. No one was likely to "expect them to know the basics of their religion" as you say. They generally weren't policed - as often occurred in many historic Christian and Muslim societies. People existed within their belief system because it was a seamless part of their culture. There were exceptions: Roman society, for example, expected everyone to show deference to aspects of the state religion, while allowing people to believe what they wished privately, but this was more a public political act rather than an expression of faith and religion.