Think in terms of introduction, body and conclusion before starting an extemporaneous essay. This way, when a topic is proposed, you can organize your thoughts to fit the format.
Develop a broad base of knowledge to work from. Often, it will be assumed that you have a command of certain topics before you are asked to write a spontaneous essay. If you are writing the essay for a course, be sure to study all the materials thoroughly.
If the essay will come up in a standardized test there is no easy way to prepare. However, knowledge of the mechanics of writing and of the essay format will serve you well. You may try to broaden your base of knowledge by reading widely both in media and in scholarly books.
Practice writing. The more practice you have, the better your expository writing will be. Practice by doing some free writing prior to the time you expect to write an expository essay. Use the practice time to see where your writing becomes too vague and where you tend to "write around" a topic. Train yourself to be as focused as possible, diving straight into your topic.
To find a topic for practice, use the newspaper or television to give yourself a prompt. Once you have a particular topic, ask yourself a specific question and then start writing.
Learn to manage your time while writing. Allow a good deal of time to create a focused introduction and thesis statement. From this, your main body should flow fairly naturally. Keep your conclusion in mind as you write. The conclusion should wrap up the whole essay and shouldn't take too much time. You should balance the time allotted with the maximum given to the introduction, less to the body and least to the conclusion.
Relax. When you sit down to write, avoid feeling too pressured. Deep breaths will help you relax and focus on the essay at hand. You may also wish to work on your posture to ensure that you are as comfortable as possible while writing.