Brainstorm and come up with a topic. "Why you should be chosen," is extremely vague. Since these essays tend to be short, about 500 words, you need to come up with a more specific topic that accurately explains why you should be chosen. You are best off choosing something that you are passionate about that you enjoy writing and talking about.
Write some rough ideas as to how your topic shows that you should be chosen. If, for example, you are a keen horseback rider, you should apply this to a quality that the institution wants, such as your perseverance in getting back on after you were thrown off, or the fact that you don't just ride horses but also care for, feed and generally look after them, which shows your dedication to and commitment to the entire task. Make sure you apply your topic to something relevant to the institution.
Ensure that your essay is personal. Your GPA and SAT scores are in the rest of the application, but the essay is a chance for you to show the committee who you are as a person, not how you perform academically.
Outline your essay to make sure the argument is clear. Even though these essays are strong, personal experience essays, they are still essays, which means that they need to have a clear argument that is backed up in each supporting paragraph. Every heading in your outline should relate to your argument and every subheading should back up the point made in your heading.
Draft the essay from your outline. Remember that it's a personal essay, which means it can (and indeed should) be full of personal stories, rich imagery and other facts that give the admissions committee an idea of who you actually are as a person.
Let the essay sit for a day or two, and then go through it with a red pen, making sure that all the spelling and grammar is correct and that the arguments are clear.
Rewrite where necessary and turn the essay in.