Satire is the "use of humor, exaggeration or ridicule to expose people's stupidity or vices." An author creating a fairy-tale satire needs to have his object of ridicule firmly in mind -- a political figure, a celebrity, a known authority -- and what form of "vice" or "stupidity" the fairy tale will expose. Remember as well that, despite its satiric thrust, the result must have the form of a fairy tale.
Two Masters of Fairy Tale Satire
The best satirical uses of fairy tales are found in the works of Jon Sciezka, who wrote under the "Fractured Fairy Tales" label: his classic is "The True Story of the Three Little Pigs," where the wolf proves himself innocent by assuming a "victim mentality." Another masterly example is the "Politically Correct Bedtime Stories" of James Finn Garner, which uses women's rights -- including reproductive rights -- sexual impotence, irrelevant lawsuits and "green" policies to make its satiric points.
The beginner at fairy tale satirism would do well to emulate the basic formulas for Sciezka and Garner, in the following steps:
A. Select two or three persons or ideas to satirize: for example, the Obamacare health plan and frivolous lawsuits.
B. Select a fairy tale or nursery rhyme -- many will be appropriate -- to rewrite. H. Dumpty, say, as the victim of an unfortunate accident.
C. Re-cast the story with characters that, in addition to being bears, wicked witches or princesses, also carry modern sensibilities.
The Satire Comes at the End
Write the tale pretty much as written in the original, up to the point of climax -- if you don't remember Dumpty, he's in Lewis Carroll -- and add a new twist, code or epilogue. Dumpty has insufficient health coverage under Obamacare, and expires. His family retaliates against the hospital with a lawsuit, charging negligence resulting in Dumpty's death. An investigative team is formed to examine Dumpty's carefully preserved remains under the latest scientific heat-fired spectroscopes. Their verdict: delicious with salsa.
Satirize the Tale and the Subject
The final twist pokes fun not only at the social institution but the fairy tale itself. Cinderella rejects her prince as a foot-fetishist; the Seven Dwarfs lose their mine because three of them are undocumented; the Queen who begs the fairies for a child in "Sleeping Beauty" hates giving over her reproductive rights. Many modern situations connect to many fairy tales; you as a writer are sure to find a glass-slipper fit.