How did Lower class American society behave in the 1920's?
Your question is rather broad, so I'd like to focus on just one aspect of the way that poorer Americans acted in 1920 that is very interesting. As the conditions deterioriated throughout the decade, gathering momentum at the end, with the loss of farmland to drought, the loss of good jobs to a faltering economy, the continuous concentration of capital into the hands of fewer and fewer people through the de-regulation of wall street, Americans tended to blame themselves.
The ethic of being able to pick yourself up by your own bootstraps had been so effectively inculcated into American society that so many people who found themselves without a job, without land to farm, without a home, they blamed this entirely on themselves. There was no real welfare system so they had nowhere to turn to and they tried to avoid bread lines and other things as long as possible given the stigma that was attached to either of those mechanisms.
If we concentrate exclusively on the behavior of the poor in their daily lives, the simplest answer to your question is that they acted the same as they did in the 1910s and largely the same as they did in the 1930s too. That is to say the lower economic classes of the time relied on family and valued it, they relied on the church and maintained their faith in God, even in the hard times. They shunned the ways of the city and the "sinful" excesses of flappers and bootleggers. They kept a stellar work ethic intact, putting in long hours at hard labor with little compensation, if they were lucky enough to have a job or own a farm. They did not blame others for their situation in life.
The book The Worst Hard Time by Timothy Egan about the Dust Bowl life in Oklahoma sums up perfectly how these people lived and acted.