In The History of 20th Century Fashion (Barnes and Noble 1986), Elizabeth Ewing describes how some women in the mid 1920s made the short and simple shift which was popular at the time by folding the cloth, making a few cuts for the  sleeves and neckline, and sewing up the edges. It's basically the same way many of us made doll dresses as children, or the way we cut peasant blouses in the 1970s (those of us who admit to being that old) before adding the elastic and drawstrings. Illustrated, it would look something like this:
(Disclaimer: The following illustrations are meant as guidelines only, and are not intended to be to scale or in exact proportions. In order to prevent sleeves from bunching up under the arms, or necklines slipping off over the shoulders, etc., you might want to do a doll-sized practice run and/or make a paper pattern you can fit and adjust.)

1. Choose a piece of fabric of a width that, allowing for short sleeves, will fit loosely enough for easy leg movement (we've just been liberated from the hobble skirt) and for covering any curves (the stylish body of this era is straight, almost boyish). The length for this style is slightly below the knee -- shorter for the more daring (the really brazen would roll their garters below their knees and put rouge on their knees), a few inches longer for older or more modest women (i.e., the ones who still hadn't bobbed their hair).

 
2. Cut away enough fabric from the sides
    to form sleeves, and cut out the neckline.
 
3. Unfold once; sew side and
    underarm seams.
 
 
 
 
 
 
 

(View when fabric is opened up

4. Face or hem neckline; hem sleeves and skirt.

Wear with flesh-colored hose (or, better: stockings and garters), seamed up the back, if you can find them (or draw a line up the back of your leg with an eyebrow pencil) and pumps with high, square heels. Women's high heeled shoes often had t-straps or straps like Mary Janes -- difficult to find, but dance shoes, or tap shoes with the taps taken off, give the look perfectly. Well-dressed women usually wore a hat, and often wore cotton, silk, or kid gloves when going out. Make-up was lip rouge (lipstick), a single color of bright red, in a "cupid's bow" (small but full, with the upper lip clearly shaped), and kohl (black eyeliner), with maybe some blue eye shadow (only the most daring and vampish overdid it) and a bit of face powder and/or rouge. Eyebrows were plucked into shape, although not as extreme as the Jean Harlow look of the 1930s, and touched up with an eyebrow pencil.