It's very easy to continually put the project off until the essay is nearly due, and in your haste to complete it you may churn out a sloppy paper. Budgeting of time is essential as the deadline approaches, and it helps to work on the paper a little bit each day in between completing more immediate homework assignments. That way, you won't feel a major time crunch when the essay is due. It helps to complete any research or reading first before beginning the actual writing of the essay.
It is important to understand the research or reading before organizing the material by making notes and highlighting key aspects of it. This helps you organize your own thoughts about the material. Think about how you want to write the essay to capture the major components of the material in a cohesive flow. This is best accomplished by putting together an outline that represents your organization, which you can adjust as necessary as you delve deeper into your reading or research. Outlines should include the main components of the paper --- introduction, body and conclusion --- and should feature important ideas and arguments that you wish to highlight in your work.
If you find yourself having difficulty piecing the material together into a cohesive flow, search for other essays written on the same subject matter. This will help you understand the best ways to present the information. You can study how the writer introduces the subject, provides coherent information about the idea in the body of the essay and then wraps it up with a clear conclusion. Compare your work with that of the other writers to help expand what you have already written, taking care not to plagiarize the other material.
The first process of editing should involve making sure the "guts" of the paper work together --- that the introduction adequately introduces the body of the paper and that the conclusion summarizes the essay. In addition to inspecting the paper closely for spelling and grammatical errors, you will also need to double check that any footnotes that cite references are in the proper locations in the essay.