An expository essay is one that explains, describes, or informs. It lists events in chronological order and tells how to do something, such as giving directions to a destination or how to make something. You use words such as first, next, and last. You need to stay focused on your topic and give the directions, explanation, or description in the order they should be given.
A persuasive essay is one that expresses an opinion, usually on an issue that is debatable. There are two clear sides to the issue, and the writer chooses one side and persuades the audience to believe the way he/she does. You should have good reasons, facts, or data to support your opinion. Generally, the strongest support for your opinion comes last, as that is what the reader will remember last.
As far as structure goes, it depends on how many paragraphs your essay is. In an essay, you need to have an introduction, body, and conclusion. The introduction should include a general statement of what the topic is, your opinion, and one or two bridge sentences to connect to your body paragraph(s). The body contains the reasons, facts, and/or data that support your opinion. The conclusion sums up your essay, bringing it to a close. Most essays assigned to students are three, four, or five paragraphs. The only difference between them is the number of body paragraphs contained in each. A three-paragraph essay has an introduction, one body paragraph, and a concluding paragraph. In a four-paragraph essay, you would add one extra body paragraph, and in a five-paragraph essay, you would have a total of three body paragraphs.