How do people know they are in this society?

Did you mean "who they are in this society?" People were genetically made to fit into a hierarchy of groups in the society. If you were an Alpha, like Bernard, you would already have the traits (at least intellectually) that an Alpha needs. The same thing applied all the way down to the Epsilons, who even had physical characteristics that identified them as Epsilons. Your identity in life was pre-determined in a test tube.