Before you start filling out the miles of paperwork that go into graduate school applications, consider your scores. (Depending on the major you are working towards, you will be required to take GRE, GED, MCAT, or LSAT, to name a few.) If you have average scores, chances of getting into top schools (Harvard, Yale, Princeton, etc.) are not that great. However, if you have your heart set on a school of that caliber, do not hesitate to apply. Often, community service, extra-curricular activities and prior performance within the field will weigh-in heavier than the graduate exams.
If you do poorly on the exams, do not get discouraged. Standardized tests are difficult for many people. Consider taking a prep course for the particular exam you are preparing to take or purchase a prep book like, Cracking the GRE published by The Princeton Review. These courses/books help you focus on the skills you need to improve upon as well as teach you strategies for answering questions that seem vague.
In addition, your letters of recommendation can help explain extenuating circumstances. Having a professor who knows your work well and can advocate for you is a great asset.