The first step in writing a persuasive essay is choosing a good topic. A good topic or thesis is one about which educated people will disagree. In other words, you cannot write a persuasive essay on a generally accepted point -- for example writing against drunk driving or in favor of recycling is pointless, because the overwhelming majority of your audience already agree with those stances. It's also a good idea to steer away from the more trite and obvious topics such as legalization of marijuana, the death penalty, abortion, etc. There is very little chance you will have anything new or interesting to say about such topics. Instead, find some small local issue that you can research in depth, such as whether one park in your town should be converted to an off-leash dog park, or whether the school cafeteria should participate in Meatless Monday.
Next, you need to do research on your topic, finding authoritative sources. The more you know about your topic, the more convincing and professional your writing will sound.
Next shape your essay carefully, using the first paragraph to capture the attention and goodwill of your audience and set out your basic thesis. In the main body of your text, use a wide variety of arguments to support your thesis, paying close attention to what sort of arguments are most likely to appeal to your audience.
Think of any possible counterarguments to your main thesis or supporting arguments and make sure to refute them, and then conclude with a call to action or appeal to the emotions of your audience.
Make sure to edit carefully, eliminating excess verbiage and correcting any spelling or grammatical errors. The hallmark of professional writing is crisp, concise prose, clearly focused on the topic at hand.