[I'm tutoring the son of one of my dad's old colleagues in writing. In preparation, I got overenthusiastic and wrote this little lesson, totally inappropriate for a freshman in high school.]
Let's consider two domains that are typically considered distinct, content and form. If you'll allow me to be a bit free and easy with some mathematical terms, I would like to suggest that writing should operate primarily on or at the intersection of content and form, and strive as far as possible to make them coextensive. The essayistic aspiration is a unity of form and content, not a disjunction.
To collapse these terms is to expand the scope of analysis. To bring the essay into view we need to step back, to introduce (at least initially) some distance. To this end, let's begin with an allegory: the essay as a sort of literary investigative report. First and foremost, the essay is the construction of a case, or an argument, which draws evidence from an archive. The OED defines essay as "[t]he action or process of trying or testing," as in "[a] trial, testing, proof; experiment." One builds a case with respect to an open question, a question which demands an answer. But writing is neither properly forensic nor scientific. While the best questions demand answers, they do not admit them. However it unfolds, the essay remains always in process as ein prozeß. "Case closed" is not something a writer can produce in good faith.
The primary value of the essay, then, is in openness. But where does it begin? It is important to remember that the essay as form is historically determined. Whether you are aware of precedents or not, the field of your writing is always already circumscribed by the work which has come before. If you pretend to write in a vacuum, your writing will amount to a sum of reactions to unarticulated stimuli, whereas if you take careful account of the essay as an historical form, you will be able to write in response to your forebears. Openness is a positive disposition toward the possibility of dialogic exchange. If you close your subject [I use this word to indicate an opposition between subject and object. Never forget that you are not perceptually privileged. Anything that you can see can see you in turn.], you foreclose the future. The work of the essay is as much in posing new questions as in positing answers.
You should always take care to do justice to your subject and in the name of your subject. You sign your writing, and it is as important to recognize the debt of your signature as it to recognize your debt to language. You have received language; it is a system that you work within. While your signature is somehow unique, it has value only in relation to what it is not, who you are not. This is another way of expressing the imperative do not pretend to write in a vacuum: it is impossible in any case. The essay is a form of address, and as such requires addressees as well as addressors. Consider well who and what you call, who and what calls you.
[Apologies to Theodor Adorno for cribbing the title of "The Essay as Form," which you can download in PDF here.]