Research the school and the graduate program where you plan to apply. Find out about accolades, past prominent graduates and the focus of the research for the program. Applicants need to be knowledgeable about the college if they plan on impressing admissions officers. The more information the better.
Create an outline of the important parts of the school and program that you want to talk about as well as personal achievements you want to highlight. It's OK to have a long list, you can go back and remove some if there isn't room. The most important aspect is not to miss something.
Think about the introduction and how you want to tackle it. The introduction is your statement of purpose, not a personal statement, so don't tell them too much personal information and instead focus on why this type of research interests you. Feel free to be a little funny and let your personality shine through.
Write the academic biography in a way that is informative, but not boring. Do not only tell what classes you have taken, but also who your mentors were and what kind of insights your classes have given you about the subject and your research.
Talk about your research project in detail and why this program is the best one for you. You are one of possibly hundreds of applicants, so what makes your research project stand out and why is this the only program that can give it justice.
Tell why their school is the best for you as a graduate student. This is not about your graduate project, but about the school itself. Discuss why its high standards of education and academic prowess makes it the best place for a person like you.