Understand that the goal of most written arguments is not to prove that you are absolutely right (or that the other side is absolutely wrong), but to show that your ideas are reasonable. The best arguments point out their own flaws and show the other side's validity.
Determine your position and audience before you begin to write. Your position is what you will argue for. Your audience is the ideal audience for your essay, and defining it will help you know what approach to take in your writing.
Gather sources and evidence for opposing positions as well as your own. Obtain enough sources and evidence so you have a strong overview of your topic, rather than just sources that support your current position.
Become familiar with opposing points of view. Spend time understanding why people hold beliefs other than yours. Though it's tempting to dismiss them as ignorant or uninformed, especially when arguing about something close to your heart, most opposing points of view are at least as reasonable as your own.
Present your thesis clearly at the end of your introduction. Your thesis needs to present your position as clearly as possible. It's helpful to include your reasoning in your thesis as well.
Portray the opposing side fairly and accurately. When you present those who disagree with you fairly, your audience will trust you more readily. Additionally, readers who disagree with you will keep reading if you show that you've taken the time to present their point of view accurately.
Stay objective. The fact that you believe in something doesn't make it correct, so don't try to argue from a personal point of view. If the position is accurate, there is evidence and logic that can support it.
Support your position with evidence and logic. Every claim you make to further your position must be supported.
Acknowledge the limitations of your position. Almost every position has its flaws. Address these flaws and limitations overtly, or your readers will. However, at the same time, show why these limitations do not affect the reasonableness of your position.
Review your work for sweeping generalizations and other fallacies. Seeking out each common fallacy in your draft is a good practice, since most of us use fallacies at times in our arguments.