Choose a topic. Look for subject matter that is already ironic or ridiculous. Much like a caricature artist exaggerates the facial features of his subject, your goal is to bring out the absurdity in your topic. You might try looking in your Sunday paper at political cartoons to get ideas for subject matter.
Use hyperbole to make your point. Hyperbole is a literary device that exaggerates facts. It does not, however, mean lying. You need to stick to the facts, but use hyperbole creatively to highlight the absurdity behind them. An example line might be, "Andy Garbo drinks tons of coffee a year to make sure he keeps his stock in Folgers profitable." This is obvious hyperbole, but it's used to make an exaggerated point about Andy.
Use irony to present your ideas. Irony is the use of words or phrases to express the opposite of what you truly mean, or to express an incongruity between what someone expects and what actually occurs. A simple example of irony would be, "He's kind enough to steal from the poor to feed his pockets." The use of "kind enough" turns this into an ironic statement. Irony is a good tool to use in satirical essays because its sarcastic tone.
Aim for humor in your satirical essays. Not all satire is funny, but by pointing out the ridiculous elements of your topic, you can often bring people over to your way of thinking or make your point quicker. A lot of readers respond faster to humor, especially when you can make them see the absurdity the same way you do.