The Flapper era was a very defining era in fashion. Women wore shorter dresses, discarded the corset and cut off their hair. Dance became the craze and sophistication was key. You can find more information here: http://www.fashion-era.com/flapper_fashion_1920s.htm
Much like today, people wore clothes in the 1920's. Of course, they were much more modest. Women still wore dresses for the most part. There were flappers in the 20's, and they wore shorter dresses. For men, suits were very popular.