Understand who you're writing for. Your job is to relate your life to what the people giving the scholarship stand for and who they are. Know your audience, and keep this in mind as you write your essay. Look for clues to who your audience is by looking at the granting organization's mission statement, biographies about people they honor, and the essay statement or question you must address.
State your thesis. Make it clear what you're writing about by writing a sentence or two at the beginning of your essay that explains what you're trying to convey to your readers. Don't use phrases and sentences like, "In this essay, I will demonstrate. . .," or "Here are the reasons I deserve this scholarship." These are overused by article and essay writers. Keep it simple, and say what you think in your thesis bit.
Develop your theme. Always keep the essay topic in mind as you're writing. There's no need to go off on a tangent about something that has nothing to do with your thesis. Provide examples from your personal life, or examples that support your thesis. Essays will usually be about you or about a specific topic handed to you by the scholarship or grant organization. Stay focused on what the reading committee wants to hear.
Keep your tone conversational. You don't have to use SAT vocabulary you learned your senior year to impress the judges. Make sure you don't come across with an "I've been through really tough situations in my life, so I deserve this scholarship" attitude. Tell the judges exactly how you've overcome your struggles and how you've risen to the top.
Conclude your essay by summarizing what you've written. Then offer something new. Give your audience something to think about, something to take away with them. If you've described how to save the whales in your essay conclude by suggesting how you think you can accomplish the steps you've just written about. Give them a new statistic backed up by a credible source.
Proofread. This cannot be emphasized enough. Grammar, punctuation, spelling and mechanics are all vital to the success of your essay. Have a friend read through it, or even your English teacher. Make sure you've stayed on topic and answered the question, or addressed the statement given by the scholarship organization.