Make a claim in your introduction, stating clearly what your argument is. Tell your audience or readers, in simple terms, what you are going to do. For instance, if you are arguing against capital punishment, you could say that you are going to present supporting evidence and, hopefully, convince the reader that capital punishment is morally wrong and is not an effective deterrent. Present your point strongly.
Present evidence to support your claim in the main body of the argument. If possible, use more than one type of evidence. You could, for instance, present some statistics to support your claim and cite a report by an expert in the area. Be consistent in your argument. Be careful not to throw everything you know about the subject into the argument. Rather than strengthen the argument, this will dilute it.
Mention the counterarguments. Try to think of what your opponent might say, and say it first. Pay due attention to these points and deal with each of them. Think of your audience or readers. If you are, for instance, presenting an academic argument, be aware that the person you are addressing will probably be an expert in the subject. She will be more impressed by your argument if you argue in a clear way and understand supporting evidence than by the amount of information you give.