Be sure to do research. Get facts and stats. Look at both sides of the issue before you establish your opinion. Look for arguments from a variety of sources. Do not rely exclusively on any one medium. Professional journals are some of the best.
Organize your essay in a way that makes sense. Read your essay to yourself aloud. If it sounds right to your ear, it is probably right. Organization has a flow to it, and your essay should flow. Point should follow point. As you introduce your arguments in the first paragraph, discuss them in the same order in the paragrpahs after.
Lose the first person language. Your essay is you speaking. It is redundant to say, "I am going to tell you what I think and this is it." Using the first person in an essay is doing exactly that. So just say what you have to say in direct statements. Read over your essay several times outloud to make sure it sounds right. Check spelling, grammar, and punctuation last. These things are not trivial; if you can't use proper grammar, people will be less likely to trust what you're saying, but you need to be certain your paper is contructed as it should be. To make sure you caught all those little mistakes, it helps if you have someone else read it, and it helps you if the mechanical parts of your writing is the last act you perform on your paper.
Make a nice, clean final copy. It helps if you have it typed up nicely. Picking a standard block font and maybe adding some graphics can help the appeal. Do not go overboard on the graphics though. Use only what supports your work, and cite it.
Proof read it several times. Stick to your topic. Keep it simple. Follow the rules or guidelines for the essay. Give support to your ideas.