Write down why you think you should appear on the show. Point out how your story would fit into the show and be beneficial to other people. You will need to mail this in addition to anything else that may help them choose you, such as a video, a book you wrote or a sample of a product that you want to show Oprah. Send these things to the producers of the Oprah Winfrey show.
Look on the Oprah website for the list of topics that they are working on for an upcoming show as well as for upcoming issues of Oprah's magazine (see Resources below). If you feel your story could fit into any of these topics, you can submit your story through the website.
Remember that Oprah and her staff pay close attention to the media. They are always looking for new ideas for the show and the magazine. Therefore, if you can get yourself and your story in the media they might see it and come looking for you. In addition, remember that the Oprah Winfrey show is filmed in Chicago, so if you can appear in any Chicago area media, that would be ideal.