Long post warning!
1. Read and understand the prompt (if any is given).
2. Formulate a thesis (essentially a knee-jerk reaction to the prompt)
3. Corroborate your thesis with examples, evidence, logic, etc.
4. Conclude the essay, making sure to affirm the value of the prompt
This is the method for composing essays not only for scholarships but for school assignments.
A 500-word essay limit should be about 5 paragraphs long.
Find your voice: formal or informal. An essay about a current issue (social, political, etc.) should be formal, that is, NO FIRST PERSON! Use third person in a formal essay. (Note: this post is mainly about formal essays)
Use a word processor. Microsoft Word 2007-2010 is useful for tracking how many words you are using and includes a spellcheck and thesaurus.
Don't use a word if you don't know what it EXACTLY means. Consult a dictionary if not sure.
Formal essays often require citation of sources. Research the latest MLA, APA, and Chicago-style citation methods. Son of Citation is a useful tool for the lazy, but make sure it's accurate!
Research may be required for an essay, especially if it's a topic you're not well-read on. Be careful what sources you use on the internet; the best suffix to look for is .edu. This means it is a collegiate or educational website.
If a sentence is giving you trouble, rewrite or scrap if needed.
If you want to express your opinion without first person, consider using the subject "one." Example: "One might wonder why Noah Webster decided to create a whole new dialect of English for the United States." This expresses a thought or emotion you felt without saying you actually thought or felt it.