I made myself a Great Gatsby-esque dress in anticipation of the movie coming out. My goal was to make something as historically accurate as possible while still using stash fabrics. I ended up making this for less than $15, but used pattern pieces that were still based on extant garments from the era.
Make a slip.
I used the tutorial on American Duchess to make a simple 1920s slip. I embellished it with lace to pretty it up a bit.
Make the overdress.
The shapes of the 1920s are thankfully easy. The bodice is just a tank-top shape, similar to Colette Patterns' Sorbetto, but without the dart. If you use the Sorbetto pattern, you'll need to extend the length quite a bit to bring it down to your hips for the dropped waist look.
For the skirt, I just sketched a curved arc (similar to a half-circle skirt pattern) where the inner arc was the same length as the width of my bodice piece's bottom edge, and the sides were as long as I wanted my skirt to be (mine was 23"). If you angle out the sides more (a curvier arc, if you will), the bottom of the skirt will be fuller and it will look more flared. I've found sewing patterns from that era with full circle skirts, so anything's a possibility! Alternately, you could use a gathered rectangle if you want to go for a simpler pattern-making process.
If you use chiffon or some other floaty, drapey fabric (and I wouldn't really recommend anything else) for the overdress, you might want to use French seams to keep things neat inside. I hand-overcast my seam allowances so that they would be as unobtrusive as possible, since my fabric was so sheer.
I finished my edges with self-fabric bias binding, but you may want to use a more stable fabric than chiffon on yours, since my binding was a mess!
I made a sash (just a long rectangle) to go around the dropped waist. I tacked it onto the side seam by hand.
The head sash is just more of the same, plus a little feather clip from the mall. Add a string of flapper-esque beads and you're all set!