Read your essay out loud. No matter your writing skills level, you'll make mistakes. You're likely to overlook mistakes in spelling, grammar and punctuation after looking at the same essay for a long time. You are more likely to catch mistakes and ways to improve if you read it out loud.
Spend some time away from your essay after you write each draft. This will give your mind time to relax after the pressure of writing. You're more likely to feel refreshed when you return to it.
Keep everything you write for your essay. Use the cut-and-paste tools to move anything that seems like it doesn't fit at the moment. Although the temptation is to just delete it, you may want to incorporate a section of your essay that you didn't know you would. Having something you already wrote available will save you time during your revisions. Delete what you didn't use only after you are confident that your essay is complete.
Ask a friend to read your essay. A point that seems clear to you may not be as clear to an outside reader. Invite your friend to ask questions about parts of your essay she doesn't understand. These questions may help you realize what you really meant to write in the first place.
Use different colors for different main points. This is especially helpful if your essay requires research. Colored pencils, pens or markers will give you a visual reminder of what information goes where in your essay.