* Research a lot of stuff on it, including things that seem orthogonal or at best tangential. Interview people, chase down primary sources, etc. Keep an eye out for surprises (in the Paul Graham sense [1]): new information that expands, challenges or outright debunks something I believe about the topic.
* Free-associate and try to tease out some dimensions along which the information can come together.
* Gradually settle on a thesis that's strongly enough supported by the evidence for the type of writing I'm doing.
* Get a good night's sleep. (Crucial step - do not skip!)
* Write a draft in the morning when my mind is fresh and the system of supporting arguments and information is still present. This may take one or more mornings depending on the length of the paper.
* Edit and format the draft, insert references, etc. Then set the paper aside and do something else.
* A day later or so, edit the draft again to cut out the fat, streamline the structure, fix spelling and grammatical errors, and so on.
* If it's intended for publication somewhere, give it to a friend to review.
* Make final edits and then submit.
Obviously, the size and complexity of this exercise depends on how big the subject is and how long the essay is going to be.