According to the University of California at Berkeley's tips on writing a graduate school statement, the overall purpose is to persuade the selection committee that you are the ideal candidate for its program. Committees are looking for motivated, driven individuals who have a high probability of succeeding in graduate school. Keep this in mind as you write your statement.
Many graduate programs will ask questions such as, "Why is this program a good fit for you?" and "Why have you chosen this field?" When answering such questions, avoid general statements and provide specific, tangible examples. Research the program thoroughly, so you understand how it differs from the rest.
After brainstorming ideas, begin by creating an outlined version of your essay. This may be done in outline format or more informally by breaking the paper into smaller sections, for example, "My background" or "Why I chose this program." Be sure to address every question that is asked.
Write your first draft. Do only a little at a time and take breaks if you become frustrated. After a draft is complete, revise it by removing any general or cliche statements, and of course, review for grammar, spelling and punctuation. Repeat this process until you have a draft with which you are happy.
Have others read your essay. Parents and friends are a good place to start. It is also a great idea to have someone from your field, perhaps a current professor or adviser, read your statement and provide feedback. Listen to their suggestions and adjust your essay as needed. After making final revisions, you should have a winning graduate application essay.