I have always tried to teach students a standard structure in writing an essay. Have a good thesis statement: it can have a "hook" as Ms. Hardison so aptly points out, something that grabs the reader. It can be a quote or a piece of attention-grabbing research, etc.
The essay needs to have some organization. I always tell students to choose the form that best suits them, but I prefer starting with the least important item of the discussion in the first body paragraph, with supporting details!!! for each item.
In the second body paragraph, I focus more on the next most important aspect of the writing, and support it with specific details to "prove" that my standpoint is logical and accurate.
I save the last, most important point for the third body paragraph (which is the essay's fourth paragraph if you're doing a five-paragraph essay.) It, too, needs supporting details.
I make sure each of the body paragraphs has a topic sentence so the reader knows what is to come in that paragraph.
The last paragraph is the conclusion: here you summarize without introducing new information or summarizing all the details you mentioned before. You can mention the primary points, but no supporting information here. It is good to have a "clincher," in this last paragraph—something that sums it up for the reader: perhaps a quote or a play on words...something clever, but nothing that will ruin your credibility as a writer.
As an example, I answered a posting recently about how important language is in the Prologue in setting the mood for the tragedy to come in Romeo and Juliet. In the conclusion, I stressed again that the language in the Prologue had been carefully chosen, but also introduced the audience to the tragic elements while setting the mood. I mentioned that language helped Shakespeare "set the stage" for the story he was about to tell. It's not brilliant—perhaps it's predictable—but as it's about a Shakespearean play, I felt it "worked."
After finishing the essay, then proofread three to four times! It can always be better. Watch subject-verb agreement, stick to one tense, and watch the use of pronouns—if the subject is singular, the pronoun must be also.
Also, do not go overboard with quotes: no more than 10 percent of any paper should be reflected in quotes: check this with your teacher.