First, you must pick an organizing principle that will act as your topic. An organizing principle is the way in which you actually sorted a group of people or items, not the actual categories themselves. Be sure that you categorize the people or items usefully so the reader can understand and identify the categories in the future. Use only one organizing principle so you don't confuse your readers!
Secondly, you must pick your purpose for writing the essay. The purpose will help your readers understand the organizing principle, and it will also serve as your main point for writing the essay.
Thirdly, pick the categories for your organizing principle. This will act as the main support for your essay! Be sure you have enough examples or explanations in each category to further support your point. For example, if you are categorizing people by social wealth, you'd have to name several people who are upper class, several people who are middle class, and several people who are lower class and explain the benefits and disadvantages of each one as support.
Now it's time to write the actual essay. This can be a tad bit tougher than most essays because you can organize it any way you'd like. Be sure the organization makes sense so that your readers can follow your essay easily. Be sure to use proper transitional phrases to ensure your essay is fluent enough to understand.
Be sure to have a strong thesis! Include a strong thesis in the beginning of your essay so your readers can understand what you will be discussing within the actual body of the essay. A thesis in a classification essay blends together your organizing principle, purpose, and categories! Be sure to restate your thesis in your conclusion to remind your readers.