So when historians talk about Greek religious practice centered around one god, group of gods/divinities, or heroes, etc, they call it "cult." Like the "cult of Demeter" or "hero cult." I assume that what you are really asking about is mystery cults specifically. The issue with knowing anything for sure about mystery cults is that it was taboo (and also illegal) to talk or write about them. First off, they weren't really secret as in people didn't know about them, they were secret as in the uninitiated weren't allowed to know what happened in their ceremonies. However, while we aren't sure exactly what happened in some of the mystery religions, we do know a little bit about admission. Sometimes you had to meet certain requirements liking being a certain age or a citizen and not having committed certain crimes. Most important perhaps though, is that you paid the initiation fees. In later ancient Greek history, when mystery cults are no longer so closely tied to specific citizens, there is evidence that even people who would not have formerly been allowed to participate (such as slaves or freedmen) can be initiated into mysteries if they can pay the dues.