Tip #1 - Ask your friend, advisor, parent, sister, and whoever else is willing, to double check your materials for typos and errors. A silly typo or mistake probably won't eliminate you from contention, but you want to do what it takes to look professional and put together. But don't let anyone write your application for you. If your family is anything like mine, they will have a lot of experience applying for undergraduate programs, but won't have a whole lot of experience applying to graduate school.
Tip #2 - A Statement of Purpose is NOT a Personal Statement. Graduate school applications are different from applications for undergraduate schools. A graduate program committee really doesn't give a shit about your sob story about losing a pinky finger shortly after your family came to the United States. They don't care about your battle to lose weight and what it taught you about the meaning of life. Unless you're applying to a program related to saving the whales - they don't really give a crap about your quest to save whales last summer in the Pacific Northwest. What they care about are your research interests and goals. Why have you chosen this program? Kisseyface University has an outstanding group of scholars whose research interests coincide with yours. Explain in some detail what you're interested in and how it relates to their work.
Tip #3 - Do your best on the GRE. Take a class if you need to. At the very least, purchase a study book and take practice tests. The GRE is weighted differently by different fields and programs. But nearly across the board, GRE scores are used when weighing applications for university wide fellowships. How else are committees supposed to weigh applications from different departments and fields? Nearly every field (not including professional programs and medical schools of course) utilizes the GRE in admissions, so university administrations often find themselves using the standardized test to determine who should win competitive fellowships.
Tip #4 - Be humble and modest. For every graduate student admitted to certain programs, there are as many as 14 capable students who get turned down. Odds are that you will get rejected at one or more programs to which you apply. Don't refer to a school or program as a "safety".
Tip #5 - Talk to other people you may know who have either attended graduate school or those who are applying about their experiences.