Argument Technique:

Some experts make a differentiation between argument and persuasion that might be somewhat useful when you determine the purpose of any argument you present: The difference is in the approach – argument primarily uses reasoning as a tool for development, while persuasion uses emotions and beliefs.  Whether you engage in persuasion or argument depends on the claim you’re making, and whether your audience is more likely to be engaged with their hearts and souls, or their heads. 

The importance of audience and tone
Since you are trying to win over a certain audience, it’s good to have a picture of that audience in mind when you sit to write.  You aren’t trying to convince someone who already agrees with you – that would be a waste of time.  Who might disagree with you, and why?  You might try to imagine yourself in that person’s shoes, and anticipate some of the reasons why they might feel as they do.  Keeping your audience in mind will also help with tone.  In your argument, you want to seem as reasonable as possible.  Calling anyone who disagrees with you an idiot, or taking other pot shots at your opposition, is a risky move.  You run the risk of alienating your audience if you start calling their judgment into question.  Instead, you must work on a way to find some common ground with your audience.  It’s a tricky balance, because you do have to consider and refute their arguments in order to make your point, but you don’t want to offend them, or you’ve shot yourself in the foot.  It’s a delicate process that requires knowing your audience and adjusting your tone subtly.
The Appeals
The three basic types of appeal in most arguments are rational, ethical and emotional.  Your subject and your audience will both help you decide what proportion of each to use in your argument.  For example, if you’re arguing that abortion is wrong, you might consider your audience:  women considering abortions or politicians with voting power?  The pregnant women might better be appealed to by way of emotion – the politician might respond better to an ethical appeal.  The appeals are what govern your choice of evidence.  Rational appeal calls for statistics, facts, logical cause and effect relationships, testimony from experts, etc.  Emotional appeal will try to arouse the opponents’ sympathies, often by including a description of some suffering or injustice.  Ethical appeal addresses our need to be part of a community.  We all want to think of ourselves as good citizens, with the good of the community in mind.  If you come off as a person of “good moral character” your audience will be more likely to trust you.  Therefore, you should avoid sounding preachy or condemning, and instead state how your opinion is in the best interest of your audience.  Any good argument must be a mixture of these appeals.  To rely on one alone is to risk losing anyone in your audience for whom that type of appeal doesn’t work.  Human beings operate on all three levels; therefore, each type of appeal has its place in any argument.  The proportions of each type are decided after considering the topic, the claim, and the audience.
Logic
Emotional appeals don’t rely on logic as heavily as do ethical and especially rational appeals.  However, any argument, no matter how persuasive with emotional appeal, must also have sound logic in order to be efficient and convincing.  Learning to spot bad logic can be a great skill for more than just academic essays and discussions.  It’s a life skill.  Some people think you need to be born with a certain kind of mind in order to be able to analyze the logic in an argument.  In truth, it’s just as simple as following a few rules for testing logic and looking for the weak link.
Toulmin Method
The Toulmin method is a great way for testing logic in any argument, even your own - especially your own.  When you argue, you try to eliminate any weaknesses in your case, and this is a good way of revealing those weaknesses.  This method asks the reader to break down the argument into three parts:  the data, the claim and the warrant.  The claim is simply the thesis – the main idea of the argument.  The data is all the evidence that develops and supports the thesis.  This should be clear so far – it’s what I ask for in every essay or response.  The warrant is a little trickier to identify, though – it’s an assumption that links the thesis to the evidence.  It explains why and how the evidence supports the thesis.  Here is an example of how this method works.

      Claim (The thesis): Leash laws need to be imposed on Santa Cruz beaches – no dogs allowed off-leash ever.
       Data (The evidence):  There are reports from tourists of unruly dogs on the beaches.  The owners aren’t in control of their dogs.  One child was nearly trampled last week by a couple of dogs.  There are messes all over the beach.  It’s hurting tourism.
       Warrant (The assumption):  If we imposed a strict leash law, these problems would go away.

This might sound like a good argument, but when you consider the warrant, it might not be so tight after all.  Simply leashing all dogs may not solve the problem of unruly dogs.  Those that don’t control their dogs now might not be willing to leash them, even if it were a law.  Those that follow the rules now and only allow their dogs off-leash during certain hours on certain beaches are most likely to clean up after their dogs already, and keep them under control.  Punishing them wouldn’t stop the problems, and it would be unfair to people and dogs who do follow the rules.

The strength of the argument rests on the warrant – if the reader or listener agrees with the assumption, then the argument is more likely to work.  If the assumption is flawed, unclear, or unconvincing, then the argument is, too.  The Toulmin method is a great tool, but not always easy to use, especially on our own arguments.  It’s hard to identify one’s own assumptions – very often, we simply accept them as “the way things are”.  In truth, most abstract ideas are relative, at least to a certain degree.  It’s worth the trouble, though:  since your entire goal is to win over someone whose opinion is different from your own, it’s important to single out points with which they might not agree.  You can’t afford to take for granted that their assumptions will be yours – they may need further convincing. 

Inductive and deductive reasoning
Aristotle developed these methods of constructing an argument.  When you reason inductively, you infer a larger truth from a series of small observations.  Example: If every tomato seedling in your garden dies when you plant before the end of April, you can inductively reason that tomatoes have a better chance of staying alive if you wait to plant them until it gets warm.  This method requires something of a leap of faith; you don't know for sure that the logic is watertight (for example, it might not be the cold but something else that is killing your plants.)  However,  if you have enough evidence, you can make an assumption.  Deductive reasoning is just the opposite – it takes a larger truth and assumes a logical conclusion for a specific circumstance.  The larger truth is called a premise.  If your premise is that tomatoes in general can't live unless the average nighttime temp is above 45 degrees, you will conclude that this year, you'll either wait until May to plant, or plant indoors.
Logical Fallacies
If you can spot a specific fallacy in any argument, you may have found the fatal weakness.  The examples in the Hacker book are not the only fallacies, but the most common ones, and ones that are fairly easy to identify once you’ve practiced a bit.  I won’t go through them here, but the book provides clear definitions and examples.  When confronted with an argument (yes, especially one of your own), try laying out the main points and checking them for these specific fallacies.

More resources for writing argument papers

A Brief Guide to Writing Argumentative Essays - Roane State Community College

How Do I Write a Position/Argument Essay? - Wheeling Jesuit University

Developing an Argument - Capital Community College