An argumentative essay can be one of the hardest essays to write. Given that many people are "stuck" in their ways, some readers may not be willing to consider alternative theories to their own.
An audience (readers) will be supportive (agrees with stand of author), wavering ("on the fence"), or hostile (completely disagreeable to information which illustrates or defines information contrary to their own beliefs).
There are also persuasion techniques that a writer must be familiar with: logos (logical), pathos (emotional), and ethos (creditability). For each of the audiences, very specific persuasion techniques work, while other techniques do not work.
For the supportive audience, support can contain both logos and pathos. The writer does not need to include any ethos (the audience already trusts the writer's creditability).
For the wavering audience, a writer must be sure to include logos and ethos. The audience needs information on the writer's creditability and on the material at hand in order to make an educated decision. Use of pathos may make the audience feel as if the author is relying on sympathy or emotions alone.
For the hostile audience, a persuasive/argumentative essay must be written with heavy application of logos (many hard to dispute facts). One must be certain to stay away from pathos. The audience may believe its use to be sentimental or irrational.
The purpose of an introduction is to introduce readers to what the essay is going to be about. Consider this paragraph something of a "get to know you" introduction (with "you" being the subject). Therefore, the introduction should include a hook (like a "hello"--an anecdote, question, metaphor, or dilemma). Side Note: Try to stay away from quotations in the introduction (at least this is what I teach my own students). Opening with the words of another person illustrates that you (as the writer) are not strong enough to begin your own writing. Use quotations to support what you are saying, not to make your points for you.
After the hook, the essay should move the reader through the argument (and why it exists in the first place). For example, the discussion of mandatory dress codes is more popular today than it has been in the past. Schools see that uniformity can be positive when it comes to recognizing who is out of place (or should not be there). Parents could save money because they are no longer having to purchase high end clothing. Students can come together with a sense of unity and school pride. Unfortunately, none of this matters. Enforcing a mandatory dress code is against both the First and Fourteenth Amendments.
As for the conclusion, the conclusion should "wrap up" the essay. One should never introduce a new point in the conclusion. Only address points which have already been brought up in the introduction or body paragraphs (support paragraphs). One must be sure to reword the thesis (not simply copy and paste it from the introduction to the conclusion).
Think of the writing process as a two funnels put together ("skinny" end to "skinny" end). The essay begins generally, moves to a very focused place (in the support/body paragraphs), and ends with a summary/generalization of the essay.
I have linked a wonderful writing site that I use with my own students below.