1) Write simply.
3) Use short words. This isn't the SAT or ACT vocabulary quiz, it's an essay. Make it readable. Don't try to wow anyone with big words. Big words are a distraction in ordinary writing. Save them for when you need them.
4) Write short sentences. As your sentences increase in length, the number of things that can go wrong in the sentences increases.
5) Bad writing is like a food stain on your shirt. No matter how good your ideas, the stain and the errors will make the strongest impression.
6) Know your point, and make your case. If you don't have a point, you're not writing a paper; you're just writing words. When you've got a point to make, state it plainly. Then help others see why they might agree with you.
7) Avoid sweeping generalizations. Go ahead and be bold in your essays, by all means. Try out strong ideas. But be clear about exactly which ideas you are presenting, and why. Avoid saying things like "since the beginning of time, this has been the case." Rather, say "this has been the case at least since 1641 when Descartes published his Meditations."
8) Edit. Then edit again. Don't think of proofreading as giving your writing a once-over before handing it in. Read what you've written, then read it again and again. Does each sentence lead into the next? Does each paragraph follow smoothly from what came before it? Is your opening line clear and compelling?
9) Love your reader. Try to put yourself in your readers' shoes. One helpful way to do this is to ask a friend to read your writing aloud to you. Listen for where they stumble or hesitate. Those are probably times where your writing is not clear.
10) Make writing a habit, not something you only do when you must. Like any other skill, the more you do it, the easier it becomes.
P.S. I've edited this post. Even after you write something, go back and read it again and keep editing. It's good exercise.