Develop a thesis for your essay: an overall purpose and a sense of the argument you wish to make. It should express a single strong idea and use logical points to back it up. Once you have a good sense of what you want to say, you can decide how you want to say it.
Write up an outline for your essay, covering all of the points you wish to make. Break the outline down paragraph by paragraph, with a single statement for the topic of each paragraph followed by a short list of subtopics embellishing that point. Examine the outline when you're done to see that it flows smoothly and has a sense of progression from beginning to end.
Write an introduction to your essay--the first paragraph in a five-paragraph format, or something longer if the essay requires it. Your introduction should provide a general overview of your chosen topic, and state your thesis as clearly and succinctly as possible.
Develop the body of your essay--the middle three paragraphs in a five-paragraph format, or more if the essay merits it--by expanding upon your thesis statement. Use the subtopics from your outline to develop the structure for each paragraph, and back up your assertions with evidence or compelling arguments. Try to provide a sense of progression from one paragraph to the next, shifting topics elegantly rather than abruptly switching from one topic to the next.
Close the essay with a conclusion--constituting one paragraph in a five-paragraph format, but no more than two or three, even in a longer format. Use it to summarize your main arguments, restate your thesis and close the essay off in a manner which provides a sense of completion.
Set your essay aside for a time--two or three days if you can--then go over it several times and perform revisions as you see fit. Tighten the prose, remove any superfluous passages and polish it so that it sounds as sharp as you can make it. If you like, you can let someone you trust read it and make constructive suggestions before finalizing your essay.