Decide on your topic and argument. Humorous essays are not really about the humor. Rather, they are about the argument and topic -- the humor is just a vehicle to deliver it. So, you need to establish precisely what you want to write about and what you want to convince people of before you start with anything humorous.
Handwrite your argument on a loose piece of paper in bullet point form. Again, stay away from the humor at this stage -- your argument needs to have the "skeleton" to hold up without humor, so you should have clear statements, explanations and examples that convince the reader of your thesis.
Decide on a form of humor you are going to use. Most people are funny in different ways; some people tell funny stories, some people express things using a funny turn of phrase, and others tell snappy jokes. You need to use your individual brand of humor to write your essay, as anything else simply won't work.
Use your humor in your essay's explanations and examples. So, you could explain one of your points using a humorous anecdote that happened to you, or by way of example you could use a humorous simile that highlights the absurdities of a situation.
Show your draft to someone to make sure that the argument makes sense and it is funny. Humorous essays need to have both elements -- a reader needs to laugh, but also walk away knowing the point you were making.
Make any necessary rewrites and print or send off your final draft.