Depending on the school and university they are going to want to know a few things about you. Where have you been, what are you doing, and how will that effect where you are going. Most of the personal statements have a key word applied to them “concision” be concise and clear cut. Whereas whimsy may be fun to read to many students try to be cute and end up cut. If the program is highly desirable and has a lot of competition make it serious and go for it.
Here is the bad thing. In general some academic support specialist is the one reading your statement and it is a check box on your way to the next step. Grades, class rankings, GRE scores and undergraduate work are likely more important than the statement. In fact I rarely see them unless I ask (acceptance happens before I get an advisee). Now I can reach down the pile and say “this one” but that is for people who have been working with me or have recommendations that have come from outside.
To write your statement an introductory paragraph of who you are and why the school is a good fit. If you’ve been working with a faculty member already this is a good point to put it.
Your second paragraph should have information about your academics and references to any papers you’ve published or projects you’ve done.
Your third paragraphs should be about jobs you’ve held, undergraduate work you’ve done, and career aspirations.
Your fourth paragraph should close out with why they should have you as a student. Accentuate your positives and make it short and sweet. Compare and contrast your academics and work experience.
Finally a conclusion and offer to answer any questions they may have.
Never ever ever ever ever (<- get the point?) say anything negative in a personal statement. Don’t worry we’ll find them. Common mistakes are things like “I did really good in Calculus even though I sucked at algebra”, of course thinking they are showing their ability to over come obstacles. I’m left thinking so you can’t do math and got lucky.