In the Jazz Age, nearly everyone danced, so they did dances almost anyone could do.
Generally, when people think about the dances of the Jazz Age (the 1920s & 30s), they bring to mind exuberant youth dances like the Charleston or Jitterbug, or the theatrical dances of Fred and Ginger.
What Fred & Ginger did was theater and spectacle, and was never intended to be an accurate representation of how ordinary folks danced. Countless examples of normal, workaday social dancing can be seen in movies of the period but not being done by exhibition dancers like Fred and Ginger. If you want to see how it was really done, look at the folks in the background or characters who are dancing to move the story along rather than to show off their skills.
The most popular dance of the period was the Foxtrot. The Waltz and the Tango were also widely danced, as were (in the '30s) Latin dances like the Rumba, Conga and Samba. The under-thirty crowd danced these mainstream ballroom styles, but also enjoyed exuberant athletic dances that would have caused most of their elders to bust a gut.
All of these dances are still part of today's ballroom repertoire. However, dances evolve over time and the dances we now call by those names are not what they were in the 20s and 30s.
Fortunately, while they differ from what is taught today, they differ primarily in that the Jazz Age dances (referred to at the time as "The Modern Dances") were FAR EASIER than their current descendents. An experienced dancer will pick them up right away, and most beginners should be able to get out on the floor with a minimum of instruction - perhaps even after just looking at these few web pages.
"And the modern dances are the most easily achieved - some absurdly simple. It was not so in Mother's time-for the steps she watched were many and varied. With her usual quiet fortitude she prevailed over a most difficult and intricate order of things - and with an application that might, in these days, be considered a mental strain."(Dancing Made Easy 1922)
A quick note on my philosophy of research and teaching: I will present my sources (largely old films, with some books and images thrown in) and make a few observations. Mostly though, I let the sources speak for themselves. You are welcome to look at the same sources and draw differing conclusions. The heart of this enterprise is making useful sources easily available, and letting peoples' interpretations of them fall where they may.
Further (and this is key) I will try to avoid defining any given thing as "correct". I will try to present the vast diversity and even anarchy of the Jazz Age dancefloor, and try to present what was typical rather than deferring to the ideas of what was proper from one of the many self-appointed dance authorities of the time (sorry Arthur Murray). Dance manuals and instructional films are valuable sources for the dance of the period, but so are films that show styles and variations not mentioned, or even scorned, in "authoritative" sources. I believe all the sources are fair game for you in selecting the elements you want to include in your own personal interpretation of Jazz Age dancing.
Variations on a Theme
One of the most striking things about the ballroom dances of the era is how like each other they are. The steps are all walks and glides (more walking than anything else), and a variation from one may be easily dropped into another. Even the Waltz seems more like a Foxtrot than what you might have seen in the 19th Century.